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Photosynthesis

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VedantPatel100

1) Definition 2) Chloroplasts: Photosynthetic Pigments and Phtosystems 3) Light Reaction: Cyclic & Non-cyclic Photophosphorylation 4) Dark Reaction: Calvin Cycle, Hatch-Slack Pathway, CAM Pathway

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๐Ÿ”๐‘ช๐‘ถ๐Ÿ + ๐Ÿ๐Ÿ๐‘ฏ๐Ÿ๐‘ถ ๐‘ช๐Ÿ”๐‘ฏ๐Ÿ๐Ÿ๐‘ถ๐Ÿ” + ๐Ÿ”๐‘ฏ๐Ÿ๐‘ถ + ๐Ÿ”๐‘ถ๐Ÿ โ†‘ ๐‘†๐‘ข๐‘›๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™
โ€ข 2 โˆ’ ๐‘™๐‘Ž๐‘ฆ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘’ ๐‘๐‘œ๐‘›๐‘ ๐‘–๐‘ ๐‘ก๐‘–๐‘›๐‘” ๐‘œ๐‘“ ๐’๐’–๐’•๐’†๐’“ & ๐’Š๐’๐’๐’†๐’“ ๐’Ž๐’†๐’Ž๐’ƒ๐’“๐’‚๐’๐’†๐’”. โ€ข ๐ต๐‘œ๐‘กโ„Ž ๐‘ ๐‘’๐‘๐‘Ž๐‘Ÿ๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘Ž ๐‘“๐‘™๐‘ข๐‘–๐‘‘ ๐‘“๐‘–๐‘™๐‘™๐‘’๐‘‘ ๐‘ ๐‘๐‘Ž๐‘๐‘’ 100 โˆ’ 200 โ„ซ ๐‘–. ๐‘’. ๐’‘๐’†๐’“๐’Š โˆ’ ๐’‘๐’๐’‚๐’”๐’•๐’Š๐’…๐’Š๐’‚๐’ ๐’”๐’‘๐’‚๐’„๐’†. โ€ข ๐ฟ๐‘–๐‘ž๐‘ข๐‘–๐‘‘, ๐‘๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘Ž๐‘๐‘’๐‘œ๐‘ข๐‘  ๐‘š๐‘Ž๐‘ก๐‘Ÿ๐‘–๐‘ฅ โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘Ž๐‘Ÿ; ๐‘๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘›๐‘–๐‘›๐‘” ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’๐‘  โ€ข ๐‘บ๐’Š๐’•๐’† ๐’๐’‡ ๐‘ซ๐’‚๐’“๐’Œ ๐’“๐’†๐’‚๐’„๐’•๐’Š๐’๐’ ๐‘œ๐‘“ ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ ๐‘–๐‘  โ€ข ๐ถ๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘›๐‘  ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก ๐‘ซ๐‘ต๐‘จ, ๐‘ ๐‘ก๐‘Ž๐‘Ÿ๐‘โ„Ž ๐‘”๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘’๐‘ , ๐Ÿ•๐ŸŽ ๐‘บ ๐’“๐’Š๐’ƒ๐’๐’”๐’๐’Ž๐’†๐’”, ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘ .
โ€ข ๐‘‡โ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ โŸน ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘œ๐‘ข๐‘  ๐‘ ๐‘Ž๐‘๐‘˜; ๐’„๐’๐’๐’•๐’‚๐’Š๐’ ๐’‘๐’Š๐’ˆ๐’Ž๐’†๐’๐’•๐’” โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘š โŸน ๐‘ ๐‘ก๐‘Ž๐‘๐‘˜ ๐‘œ๐‘“ ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐‘บ๐’Š๐’•๐’† ๐’๐’‡ ๐‘ณ๐’Š๐’ˆ๐’‰๐’• ๐’“๐’†๐’‚๐’„๐’•๐’Š๐’๐’ ๐‘œ๐‘“ ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ ๐‘–๐‘  โ€ข ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ โŸน ๐‘๐‘œ๐‘›๐‘›๐‘’๐‘๐‘ก ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘ 
๐‘‚๐‘ข๐‘ก๐‘’๐‘Ÿ ๐‘š๐‘’๐‘š๐‘. ๐ผ๐‘›๐‘›๐‘’๐‘Ÿ ๐‘š๐‘’๐‘š๐‘. ๐‘ƒ๐‘’๐‘Ÿ๐‘–๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘–๐‘‘๐‘–๐‘Ž๐‘™ ๐‘ ๐‘๐‘Ž๐‘๐‘’ ๐ท๐‘๐ด ๐‘…๐‘–๐‘๐‘œ๐‘ ๐‘œ๐‘š๐‘’ ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘โ„Ž ๐‘”๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘’ ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ ๐‘‡โ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘š ๐‘บ๐‘ป๐‘น๐‘ผ๐‘ช๐‘ป๐‘ผ๐‘น๐‘ฌ ๐‘ถ๐‘ญ ๐‘ช๐‘ฏ๐‘ณ๐‘ถ๐‘น๐‘ถ๐‘ท๐‘ณ๐‘จ๐‘บ๐‘ป
โ€ข ๐บ๐‘Ÿ๐‘’๐‘’๐‘˜: ๐’„๐’‰๐’๐’๐’“๐’๐’” = ๐’ˆ๐’“๐’†๐’†๐’ ; ๐’‘๐’‰๐’š๐’๐’๐’๐’ = ๐’๐’†๐’‚๐’‡ โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ , ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘๐‘ฆ๐‘Ž๐‘›๐‘œ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž โ€ข ๐น๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐’‘๐’“๐’๐’•๐’๐’„๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’ ๐‘–๐‘› ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘๐‘’ ๐‘œ๐‘“ ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐‘จ๐’ƒ๐’”๐’๐’“๐’ƒ๐’” โŸน ๐‘น๐‘ฌ๐‘ซ & ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ ๐’๐’Š๐’ˆ๐’‰๐’• โ€ข ๐‘น๐’†๐’‡๐’๐’†๐’„๐’•๐’” โŸน ๐‘ฎ๐‘น๐‘ฌ๐‘ฌ๐‘ต ๐’๐’Š๐’ˆ๐’‰๐’• ; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘™๐‘’๐‘Ž๐‘ฃ๐‘’๐‘  ๐‘Ž๐‘๐‘๐‘’๐‘Ž๐‘Ÿ ๐‘”๐‘Ÿ๐‘’๐‘’๐‘› ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ. โ€ข ๐‘‡๐‘ฆ๐‘๐‘’๐‘  ๐‘œ๐‘“ ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™: ๐‘– ๐ผ๐‘› โ„Ž๐‘–๐‘”โ„Ž๐‘’๐‘Ÿ ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ : ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’๐’” ๐’‚ & ๐’ƒ ๐‘–๐‘– ๐ผ๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’: ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’๐’” ๐’„, ๐’…, ๐’† ๐‘–๐‘–๐‘– ๐ผ๐‘› ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž: ๐‘ฉ๐’‚๐’„๐’•๐’†๐’“๐’Š๐’ โˆ’ ๐’„๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’ & ๐’ƒ๐’‚๐’„๐’•๐’†๐’“๐’Š๐’ โˆ’ ๐’—๐’Š๐’“๐’Š๐’…๐’Š๐’
โ€ข ๐‘‡๐‘Ž๐‘‘๐‘๐‘œ๐‘™๐‘’ โˆ’ ๐‘ โ„Ž๐‘Ž๐‘๐‘’๐‘‘ ๐‘ ๐‘ก๐‘Ÿ๐‘ข๐‘๐‘ก๐‘ข๐‘Ÿ๐‘’ โ€ข ๐‘ท๐’๐’“๐’‘๐’‰๐’š๐’“๐’Š๐’ ๐’‰๐’†๐’‚๐’… โŸถ 4 ๐‘๐‘ฆ๐‘Ÿ๐‘Ÿ๐‘œ๐‘™๐‘’ ๐‘Ÿ๐‘–๐‘›๐‘”๐‘  ๐‘ค๐‘–๐‘กโ„Ž 4 ๐‘ โˆ’ ๐‘Ž๐‘ก๐‘œ๐‘š๐‘  ๐‘กโ„Ž๐‘Ž๐‘ก ๐‘ ๐‘ข๐‘Ÿ๐‘Ÿ๐‘œ๐‘ข๐‘›๐‘‘ ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘Ž๐‘™ ๐‘€๐‘” โˆ’ ๐‘Ž๐‘ก๐‘œ๐‘š. โ€ข ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐’•๐’‚๐’Š๐’ โŸถ ๐‘™๐‘œ๐‘›๐‘” โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘› ๐‘โ„Ž๐‘Ž๐‘–๐‘› โ€ข ๐ป๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘โ„Ž๐‘–๐‘™๐‘–๐‘ ๐ป๐‘’๐‘Ž๐‘‘ โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐ป๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘โ„Ž๐‘œ๐‘๐‘–๐‘ ๐‘ก๐‘Ž๐‘–๐‘™ โŸน ๐ด๐‘›๐‘โ„Ž๐‘œ๐‘Ÿ๐‘  ๐‘ก๐‘œ ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘’ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”๐‘กโ„Ž๐‘  ๐‘œ๐‘“ ๐’—๐’Š๐’๐’๐’†๐’• โˆ’ ๐’ƒ๐’๐’–๐’† & ๐’๐’“๐’‚๐’๐’ˆ๐’† โˆ’ ๐’“๐’†๐’… ๐‘™๐‘–๐‘”โ„Ž๐‘ก. โ€ข ๐‘ƒ๐‘Ÿ๐‘–๐‘š๐‘Ž๐‘Ÿ๐‘ฆ ๐‘’๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘› ๐‘‘๐‘œ๐‘›๐‘œ๐‘Ÿ โ€ข ๐บ๐‘–๐‘ฃ๐‘’๐‘  ๐’ˆ๐’“๐’†๐’†๐’ ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘ก๐‘œ ๐’๐’†๐’‚๐’—๐’†๐’”
๐ถ๐ป2๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป2 = ๐ถ๐ป ๐ถ๐ป3 ๐‘‚ ๐ถ๐ป3 ๐‘–๐‘› ๐ถโ„Ž๐‘™. ๐‘Ž & ๐ถ๐ป๐‘‚ ๐‘–๐‘› ๐ถโ„Ž๐‘™. ๐‘ ๐‘ต ๐‘ต ๐‘ต ๐‘ต โŠ– โŠ– ๐‘ด๐’ˆ ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐‘ท๐’๐’“๐’‘๐’‰๐’š๐’“๐’Š๐’ ๐‘ฏ๐’†๐’‚๐’… ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐‘ป๐’‚๐’Š๐’ ๐‘‚ ๐‘‚ ๐ป2๐ถ ๐‘ฏ๐’†๐’‚๐’…
โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ , ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ก๐‘–๐‘ ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž โ€ข ๐ต๐‘Ÿ๐‘–๐‘”โ„Ž๐‘ก ๐’“๐’†๐’…, ๐’š๐’†๐’๐’๐’๐’˜ ๐’๐’“ ๐’๐’“๐’‚๐’๐’ˆ๐’† ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ โ€ข ๐ด๐‘๐‘๐‘’๐‘ ๐‘ ๐‘œ๐‘Ÿ๐‘ฆ ๐‘๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘กโ„Ž๐‘’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘›๐‘œ๐‘ก ๐‘Ž๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘ญ๐‘ผ๐‘ต๐‘ช๐‘ป๐‘ฐ๐‘ถ๐‘ต๐‘บ: ๐‘– ๐‘จ๐’ƒ๐’”๐’๐’“๐’‘๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ ๐’๐’Š๐’ˆ๐’‰๐’• ๐‘–๐‘– ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘ ๐‘“๐‘’๐‘Ÿ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ก๐‘œ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘–๐‘–๐‘– ๐‘ƒ๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘๐‘ก ๐‘“๐‘Ÿ๐‘œ๐‘š ๐‘œ๐‘ฅ๐‘–๐‘‘๐‘Ž๐‘ก๐‘–๐‘œ๐‘› & ๐‘’๐‘ฅ๐‘๐‘’๐‘ ๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘ฃ ๐‘‰๐‘–๐‘ก๐‘Ž๐‘š๐‘–๐‘› ๐ด ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก๐‘–๐‘œ๐‘› ๐‘ฃ ๐บ๐‘–๐‘ฃ๐‘’ ๐’„๐’๐’๐’๐’–๐’“ ๐’•๐’ ๐’‡๐’๐’๐’˜๐’†๐’“๐’” & ๐’‡๐’“๐’–๐’Š๐’•๐’”
๐‘ป๐’€๐‘ท๐‘ฌ๐‘บ: 1) ๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’๐‘ : 2) ๐‘‹๐‘Ž๐‘›๐‘กโ„Ž๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  (๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘™๐‘ ): โ€ข ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’† โˆ’ ๐‘น๐’†๐’… ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ผ๐‘ฝ, ๐‘ฝ๐’Š๐’๐’๐’†๐’• & ๐‘ฉ๐’๐’–๐’† ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐‘†๐‘๐‘Ž๐‘ก๐‘ก๐‘’๐‘Ÿ ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’†, ๐‘น๐’†๐’… & ๐’€๐’†๐’๐’๐’๐’˜ ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐บ๐‘’๐‘›. ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘ข๐‘™๐‘Ž = ๐ถ40๐ป56 โ€ข ๐ธ๐‘ฅ. ๐‘ณ๐’š๐’„๐’๐’‘๐’†๐’๐’†๐’” ๐‘…๐‘’๐‘‘ ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘–๐‘› ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘œ & ๐‘โ„Ž๐‘–๐‘™๐‘™๐‘– , ๐›ผ โˆ’ ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’ & ๐›ฝ โˆ’ ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’. โ€ข ๐ถ๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘› ๐‘œ๐‘ฅ๐‘ฆ๐‘”๐‘’๐‘› โ€ข ๐บ๐‘’๐‘›. ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘ข๐‘™๐‘Ž = ๐ถ40๐ป56๐‘‚ โ€ข ๐ธ๐‘ฅ. ๐ถ๐‘Ÿ๐‘ฆ๐‘๐‘ก๐‘œ๐‘ฅ๐‘Ž๐‘›๐‘กโ„Ž๐‘–๐‘›, ๐‘ณ๐’–๐’•๐’†๐’Š๐’ (๐‘ฆ๐‘’๐‘™๐‘™๐‘œ๐‘ค๐‘–๐‘ โ„Ž ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘œ๐‘“ ๐‘Ž๐‘ข๐‘ก๐‘ข๐‘š๐‘›๐‘Ž๐‘™ ๐‘“๐‘œ๐‘™๐‘–๐‘Ž๐‘”๐‘’), ๐‘ญ๐’–๐’„๐’๐’™๐’‚๐’๐’•๐’‰๐’Š๐’ (๐ต๐‘Ÿ๐‘œ๐‘ค๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’)
โ€ข ๐บ๐‘Ÿ๐‘’๐‘’๐‘˜: ๐’‘๐’‰๐’š๐’Œ๐’๐’” = ๐’‚๐’๐’ˆ๐’‚ ; ๐’ƒ๐’Š๐’๐’Š๐’” = ๐’ƒ๐’Š๐’๐’† โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘๐‘™๐‘ข๐‘’ โˆ’ ๐‘”๐‘Ÿ๐‘’๐‘’๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘กโ„Ž๐‘’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘›๐‘œ๐‘ก ๐‘Ž๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  & ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐‘Š๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘ ๐‘œ๐‘™๐‘ข๐‘๐‘™๐‘’ โ€ข ๐‘ป๐’€๐‘ท๐‘ฌ๐‘บ โˆ’ ๐‘– ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘’๐‘Ÿ๐‘ฆ๐‘กโ„Ž๐‘Ÿ๐‘–๐‘› (๐‘น๐‘ฌ๐‘ซ): โŸน ๐‘“๐‘œ๐‘ข๐‘›๐‘‘ ๐‘–๐‘› ๐‘…โ„Ž๐‘œ๐‘‘๐‘œ๐‘โ„Ž๐‘ฆ๐‘ก๐‘Ž (๐‘…๐‘’๐‘‘ ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’) โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ฉ๐’๐’–๐’† & ๐‘ฎ๐’“๐’†๐’†๐’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘– ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘๐‘ฆ๐‘Ž๐‘›๐‘–๐‘› ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ : โŸน ๐‘“๐‘œ๐‘ข๐‘›๐‘‘ ๐‘–๐‘› ๐ถ๐‘ฆ๐‘Ž๐‘›๐‘œ๐‘โ„Ž๐‘ฆ๐‘ก๐‘Ž (๐ต๐บ๐ด) โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’† & ๐‘น๐’†๐’… ๐‘™๐‘–๐‘”โ„Ž๐‘ก
๐‘ซ๐’Š๐’“๐’†๐’„๐’• ๐’๐’Š๐’ˆ๐’‰๐’•
๐‘š๐‘Ž๐‘‘๐‘’ ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘ , ๐‘๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  & ๐‘๐‘œ โˆ’ ๐‘“๐‘Ž๐‘๐‘ก๐‘œ๐‘Ÿ๐‘  ๐‘†๐‘–๐‘ก๐‘’ ๐‘œ๐‘“ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘› ๐‘ƒ๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’ ๐ด๐‘‡๐‘ƒ & ๐‘๐ด๐ท๐‘ƒ๐ป ๐ถ๐‘Ž๐‘๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘ƒ๐‘Ÿ๐‘œ๐‘š๐‘œ๐‘ก๐‘’ ๐‘’โˆ’ ๐‘ก๐‘œ โ†‘ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ ๐‘ก๐‘Ž๐‘ก๐‘’ ๐‘ƒ๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘  & ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘  ๐‘†๐‘ข๐‘Ÿ๐‘Ÿ๐‘œ๐‘ข๐‘›๐‘‘ ๐‘กโ„Ž๐‘’ ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘ ๐‘“๐‘’๐‘Ÿ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ก๐‘œ ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’
โ€ข ๐ท๐‘–๐‘ ๐‘๐‘œ๐‘ฃ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘๐‘’๐‘“๐‘œ๐‘Ÿ๐‘’; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐‘ท๐‘บ ๐‘ฐ. โ€ข ๐ฟ๐‘œ๐‘๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘œ๐‘›: ๐‘– ๐‘ถ๐’–๐’•๐’†๐’“ ๐’”๐’–๐’“๐’‡๐’‚๐’„๐’† ๐’๐’‡ ๐’•๐’‰๐’š๐’๐’‚๐’Œ๐’๐’Š๐’… ๐’Ž๐’†๐’Ž๐’ƒ. ๐‘–๐‘– ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ โ€ข ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ โŸน ๐‘ช๐’‰๐’. ๐’‚ ๐’Ž๐’๐’๐’†๐’„๐’–๐’๐’† ๐‘ท โˆ’ ๐Ÿ•๐ŸŽ๐ŸŽ ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ & ๐‘“๐‘Ž๐‘Ÿ ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ž๐‘ก 700 ๐‘›๐‘š ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”โ„Ž๐‘ก โ€ข ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐ป๐‘Ž๐‘Ÿ๐‘ฃ. ๐ถ๐‘œ๐‘š๐‘๐‘™๐‘’๐‘ฅ โŸน ๐ถโ„Ž๐‘™. ๐‘ + ๐ถโ„Ž๐‘™. ๐‘Ž 670, 680, 695 + ๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐’†โˆ’ ๐’…๐’๐’๐’๐’“ โŸน ๐‘ƒ๐‘™๐‘Ž๐‘ ๐‘ก๐‘œ๐‘๐‘ฆ๐‘Ž๐‘›๐‘–๐‘› โ€ข ๐’†โˆ’ ๐’‚๐’„๐’„๐’†๐’‘๐’•๐’๐’“ โŸน ๐ผ๐‘Ÿ๐‘œ๐‘› โˆ’ ๐‘ ๐‘ข๐‘™๐‘โ„Ž๐‘ข๐‘Ÿ ๐น๐‘’๐‘† ๐‘๐‘’๐‘›๐‘ก๐‘’๐‘Ÿ๐‘ 
โ€ข ๐ด๐‘๐‘ก๐‘  ๐‘“๐‘–๐‘Ÿ๐‘ ๐‘ก, ๐‘๐‘ข๐‘ก ๐‘‘๐‘–๐‘ ๐‘๐‘œ๐‘ฃ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘Ž๐‘ก๐‘’๐‘Ÿ; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐‘ท๐‘บ ๐‘ฐ๐‘ฐ. โ€ข ๐ฟ๐‘œ๐‘๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘œ๐‘›: ๐‘ฐ๐’๐’๐’†๐’“ ๐’”๐’–๐’“๐’‡๐’‚๐’„๐’† ๐’๐’‡ ๐’•๐’‰๐’š๐’๐’‚๐’Œ๐’๐’Š๐’… ๐’Ž๐’†๐’Ž๐’ƒ. โ€ข ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ โŸน ๐‘ช๐’‰๐’. ๐’‚ ๐’Ž๐’๐’๐’†๐’„๐’–๐’๐’† ๐‘ท โˆ’ ๐Ÿ”๐Ÿ–๐ŸŽ ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก, ๐‘›๐‘œ๐‘ก ๐‘–๐‘› ๐‘“๐‘Ž๐‘Ÿ ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ž๐‘ก 680 ๐‘›๐‘š ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”โ„Ž๐‘ก โ€ข ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐ป๐‘Ž๐‘Ÿ๐‘ฃ. ๐ถ๐‘œ๐‘š๐‘๐‘™๐‘’๐‘ฅ โŸน ๐ถโ„Ž๐‘™. ๐‘Ž 660, 670, 680, 695, 700 + ๐ถโ„Ž๐‘™. ๐‘ + ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘๐‘–๐‘™๐‘–๐‘›๐‘  + ๐‘‹๐‘Ž๐‘›๐‘กโ„Ž๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  โ€ข ๐’†โˆ’ ๐’…๐’๐’๐’๐’“ โŸน ๐‘Š๐‘Ž๐‘ก๐‘’๐‘Ÿ โ€ข ๐’†โˆ’ ๐’‚๐’„๐’„๐’†๐’‘๐’•๐’๐’“ โŸน ๐‘ƒ๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘ , ๐‘ž๐‘ข๐‘–๐‘›๐‘œ๐‘›๐‘’
๐ด๐‘๐‘๐‘’๐‘ ๐‘ ๐‘œ๐‘Ÿ๐‘ฆ ๐‘ƒ๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘ณ๐’Š๐’ˆ๐’‰๐’• ๐’‚๐’ƒ๐’”๐’๐’“๐’‘๐’•๐’Š๐’๐’ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘ฌ๐’๐’†๐’“๐’ˆ๐’š ๐’•๐’“๐’‚๐’๐’”๐’‡๐’†๐’“ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘: ๐‘ฌ๐’™๐’„๐’Š๐’•๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ช๐’‰๐’. ๐’‚ ๐‘ฏ๐Ÿ๐‘ถ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ’: ๐‘ท๐’‰๐’๐’•๐’๐’๐’š๐’”๐’Š๐’” ๐’๐’‡ ๐’˜๐’‚๐’•๐’†๐’“ ๐‘ถ๐Ÿ + - - ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“: ๐‘ญ๐’๐’“๐’Ž. ๐’๐’‡ ๐’‚๐’”๐’”๐’Š๐’Ž๐’Š๐’๐’Š๐’•๐’‚๐’“๐’š ๐’‘๐’๐’˜๐’†๐’“ ๐‘จ๐‘ซ๐‘ท + ๐‘ท๐’Š โŸถ ๐‘จ๐‘ป๐‘ท ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ
โ€ข ๐‘ƒโ„Ž๐‘œ๐‘ก๐‘œ๐‘™๐‘ฆ๐‘ ๐‘–๐‘  ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ & ๐‘‚2 ๐‘’๐‘ฃ๐‘œ๐‘™๐‘ข๐‘ก๐‘–๐‘œ๐‘› ๐‘‘๐‘œ๐‘’๐‘  ๐‘›๐‘œ๐‘ก ๐‘ก๐‘Ž๐‘˜๐‘’ ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐‘๐ด๐ท๐‘ƒ๐ป ๐‘–๐‘  ๐‘›๐‘œ๐‘ก ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘. โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐‘ƒ๐‘† โˆ’ ๐ผ ๐‘–๐‘  ๐‘–๐‘›๐‘ฃ๐‘œ๐‘™๐‘ฃ๐‘’๐‘‘. โ€ข ๐ด๐‘‡๐‘ƒ ๐‘–๐‘  ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’๐‘‘ ๐‘Ž๐‘ก 2 ๐‘ ๐‘–๐‘ก๐‘’๐‘ . โ€ข ๐ธ๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘  ๐‘Ÿ๐‘’๐‘ก๐‘ข๐‘Ÿ๐‘› ๐‘๐‘Ž๐‘๐‘˜ ๐‘ก๐‘œ ๐‘ƒ๐‘† โˆ’ ๐ผ.
๐‘ช๐’€๐‘ช๐‘ณ๐‘ฐ๐‘ช ๐‘ท๐’‰๐’๐’•๐’๐’ ๐น๐‘’๐‘Ÿ๐‘Ÿ๐‘–๐‘‘๐‘œ๐‘ฅ๐‘–๐‘› ๐‘…๐‘’๐‘‘๐‘ข๐‘๐‘–๐‘›๐‘” ๐‘†๐‘ข๐‘๐‘ ๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘ท๐’‰๐’๐’•๐’๐’๐’” โ†–โ†–โ†– ๐‘ญ๐’†๐’“๐’“๐’Š๐’…๐’๐’™๐’Š๐’ ๐‘ท๐’๐’‚๐’”๐’•๐’๐’„๐’š๐’‚๐’๐’Š๐’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘ท๐‘บ โˆ’ ๐‘ฐ (๐‘ท๐Ÿ•๐ŸŽ๐ŸŽ)
โ€ข ๐‘ƒโ„Ž๐‘œ๐‘ก๐‘œ๐‘™๐‘ฆ๐‘ ๐‘–๐‘  ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ & ๐‘‚2 ๐‘’๐‘ฃ๐‘œ๐‘™๐‘ข๐‘ก๐‘–๐‘œ๐‘› ๐‘ก๐‘Ž๐‘˜๐‘’๐‘  ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐‘๐ด๐ท๐‘ƒ๐ป ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘ก๐‘Ž๐‘˜๐‘’๐‘  ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐ต๐‘œ๐‘กโ„Ž ๐‘ƒ๐‘† โˆ’ ๐ผ & ๐‘ƒ๐‘† โˆ’ ๐ผ๐ผ ๐‘Ž๐‘Ÿ๐‘’ ๐‘–๐‘›๐‘ฃ๐‘œ๐‘™๐‘ฃ๐‘’๐‘‘. โ€ข ๐ผ๐‘ก ๐‘–๐‘  ๐‘Ž๐‘™๐‘ ๐‘œ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐’ โˆ’ ๐’”๐’„๐’‰๐’†๐’Ž๐’† ๐‘‘๐‘ข๐‘’ ๐‘ก๐‘œ ๐‘–๐‘ก๐‘  ๐‘ง๐‘–๐‘” โˆ’ ๐‘ง๐‘Ž๐‘” ๐‘Ÿ๐‘œ๐‘ข๐‘ก๐‘’ ๐‘œ๐‘“ ๐‘’๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘ . โ€ข ๐ธ๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘  ๐‘‘๐‘œ ๐‘›๐‘œ๐‘ก ๐‘Ÿ๐‘’๐‘ก๐‘ข๐‘Ÿ๐‘› ๐‘ก๐‘œ ๐‘ƒ๐‘† โˆ’ ๐ผ ๐‘œ๐‘Ÿ ๐‘ƒ๐‘† โˆ’ ๐ผ๐ผ.
๐‘ท๐’‰๐’๐’•๐’๐’๐’” โ†–โ†– ๐‘ญ๐’†๐’“๐’“๐’Š๐’…๐’๐’™๐’Š๐’ ๐‘ท๐’๐’‚๐’”๐’•๐’๐’’๐’–๐’Š๐’๐’๐’๐’† ๐Ÿ’๐’†โˆ’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘ท๐‘บ โˆ’ ๐‘ฐ๐‘ฐ (๐‘ท๐Ÿ”๐Ÿ–๐ŸŽ) ๐‘ท๐‘บ โˆ’ ๐‘ฐ (๐‘ท๐Ÿ•๐ŸŽ๐ŸŽ) โ†—โ†— ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐‘ฏ๐Ÿ๐‘ถ ๐Ÿ’ ร— ๐Ÿ’๐‘ฏ+ ๐Ÿ๐‘ฏ๐Ÿ๐‘ถ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’
๐Ÿ‘ ๐‘ท๐’‰๐’‚๐’”๐’†๐’” ๐‘ญ๐’Š๐’™๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’๐’๐’—๐’†๐’“๐’”๐’Š๐’๐’ ๐’๐’‡ ๐‘ท๐‘ฎ๐‘จ ๐’•๐’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ ๐‘น๐’†๐’ˆ๐’†๐’๐’†๐’“๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘น๐’–๐‘ฉ๐‘ท
๐ถ = ๐‘‚ ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐Ÿ’ ๐Ÿ“ ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ“ โˆ’ ๐’ƒ๐’Š๐’”๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† (๐‘น๐’–๐‘ฉ๐‘ท) 6 ร— ๐‘น๐’–๐‘ฉ๐’Š๐’”๐‘ช๐‘ถ ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ 12 ร— ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ) [๐Ÿ” ร— ๐Ÿ“ ๐‘ช = ๐Ÿ‘๐ŸŽ ๐‘ช] [๐Ÿ๐Ÿ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ‘๐Ÿ” ๐‘ช] + ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ + ๐Ÿ” ๐‘ฏ๐Ÿ๐‘ถ ๐‘…๐‘–๐‘๐‘ข๐‘™๐‘œ๐‘ ๐‘’ ๐ต๐‘–๐‘ ๐‘โ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘’ ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘ฅ๐‘ฆ๐‘™๐‘Ž๐‘ ๐‘’ ๐‘‚๐‘ฅ๐‘–๐‘‘๐‘Ž๐‘ ๐‘’
๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ) ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’‚๐’๐’…๐’†๐’‰๐’š๐’…๐’† (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ) ๐Ÿ, ๐Ÿ‘ โˆ’ ๐‘ซ๐’Š๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘จ๐‘ป๐‘ท ๐‘จ๐‘ซ๐‘ท ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ท๐’Š ๐Ÿ๐Ÿ ๐’Ž๐’๐’. ๐’†๐’‚๐’„๐’‰
๐‘‡โ„Ž๐‘’ 12 ๐‘ƒ๐บ๐ด๐ฟ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘  ๐‘๐‘Ž๐‘› ๐‘๐‘’ ๐‘ข๐‘ก๐‘–๐‘™๐‘–๐‘ ๐‘’๐‘‘ ๐‘–๐‘› 4 ๐‘ค๐‘Ž๐‘ฆ๐‘ : 5 ร— [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 5 ร— [๐‘ซ๐‘ฏ๐‘จ๐‘ท] ๐‘‡๐‘Ÿ๐‘–๐‘œ๐‘ ๐‘’ ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘’ ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ โ‘ก โ‘ข [๐Ÿ“ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ๐Ÿ“ ๐‘ช] [๐Ÿ“ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ๐Ÿ“ ๐‘ช] [๐Ÿ“ ร— ๐‘ท] [๐Ÿ“ ร— ๐‘ท] 3 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 3 [๐‘ซ๐‘ฏ๐‘จ๐‘ท] [๐Ÿ‘ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ— ๐‘ช] [๐Ÿ‘ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ— ๐‘ช] + [๐Ÿ‘ ร— ๐‘ท] [๐Ÿ‘ ร— ๐‘ท] ๐ด๐‘™๐‘‘๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ, ๐Ÿ” โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”. [๐Ÿ‘ ร— ๐Ÿ” ๐‘ช = ๐Ÿ๐Ÿ– ๐‘ช] [๐Ÿ‘ ร— ๐Ÿ ๐‘ท] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ:
3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ, ๐Ÿ” โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”. 3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘Ž๐‘ ๐‘’ ๐Ÿ‘ ๐‘ท๐’Š โ‘  โ‘ก ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ’: ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ฎ๐’๐’–๐’„๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ฎ๐‘ณ๐‘ผ๐‘ช๐‘ถ๐‘บ๐‘ฌ ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ ๐‘ท๐’Š [๐Ÿ” ๐‘ช] [๐Ÿ” ๐‘ช] [๐Ÿ” ๐‘ช]
2 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 2 [๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’†] + [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] [๐Ÿ ร— ๐Ÿ” ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘˜๐‘’๐‘ก๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘ฌ๐’“๐’š๐’•๐’‰๐’“๐’๐’”๐’† ๐Ÿ’ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† + [๐Ÿ ร— ๐Ÿ“ ๐‘ช] [๐Ÿ ร— ๐Ÿ’ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘
+ [๐Ÿ ร— ๐Ÿ’ ๐‘ช] [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘Ž๐‘™๐‘‘๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ• โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘ฌ๐’“๐’š๐’•๐’‰๐’“๐’๐’”๐’† ๐Ÿ’ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ• ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ”: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ 2 [๐‘ซ๐‘ฏ๐‘จ๐‘ท] [๐Ÿ ร— ๐‘ท] [๐Ÿ ร— ๐‘ท] [๐Ÿ ร— ๐Ÿ ๐‘ท] 2 ๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ• โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘Ž๐‘ ๐‘’ [๐Ÿ ร— ๐Ÿ• ๐‘ช] [๐Ÿ ร— ๐‘ท] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ•: ๐Ÿ ๐‘ท๐’Š
2 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 2 [๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ• โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’†] + [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] [๐Ÿ ร— ๐Ÿ• ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘˜๐‘’๐‘ก๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘น๐’Š๐’ƒ๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† + [๐Ÿ ร— ๐Ÿ“ ๐‘ช] [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ–:
๐‘บ๐’•๐’†๐’‘ ๐Ÿ—: 2 ๐‘ฟ๐’š๐’๐’–. ๐Ÿ“ โˆ’ ๐‘ท [๐Ÿ’ ร— ๐Ÿ“ ๐‘ช] 2 ๐‘ฟ๐’š๐’๐’–. ๐Ÿ“ โˆ’ ๐‘ท ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ– 4 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 4 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐ธ๐‘๐‘–๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ [๐Ÿ’ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ๐ŸŽ: 2 ๐‘น๐’Š๐’ƒ๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ 2 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ–
๐‘บ๐’•๐’†๐’‘ ๐Ÿ๐Ÿ: 6 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ” ร— ๐Ÿ“ ๐‘ช] [๐Ÿ” ร— ๐‘ท] 6 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ“ โˆ’ ๐’ƒ๐’Š๐’”๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ” ร— ๐Ÿ“ ๐‘ช] [๐Ÿ” ร— ๐Ÿ ๐‘ท] ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘Ÿ๐‘–๐‘๐‘ข๐‘™๐‘œ๐‘ ๐‘’ ๐‘˜๐‘–๐‘›๐‘Ž๐‘ ๐‘’ ๐Ÿ” ๐‘จ๐‘ซ๐‘ท ๐Ÿ” ๐‘จ๐‘ป๐‘ท
๐Ÿ” ๐‘น๐’–๐‘ฉ๐‘ท + 6 ๐ถ๐‘‚2 + 6 ๐ป2๐‘‚ ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ + 12 ๐ด๐‘‡๐‘ƒ + 12 ๐‘๐ด๐ท๐‘ƒ๐ป + 12 ๐ป+ ๐Ÿ๐Ÿ [๐‘ท๐‘ฎ๐‘จ] ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ๐‘ณ + 12 ๐ด๐ท๐‘ƒ + 12 ๐‘ƒ๐‘– + 12 ๐‘๐ด๐ท๐‘ƒ+ ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ๐‘ณ + 6 ๐ด๐‘‡๐‘ƒ ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ (๐‘ญ๐’“๐’–๐’„. ๐Ÿ” โˆ’ ๐‘ท) + ๐Ÿ” ๐‘น๐’–๐‘ฉ๐‘ท + 6 ๐ด๐ท๐‘ƒ + 6 ๐‘ƒ๐‘–
๐ถ๐‘œ๐‘š๐‘๐‘–๐‘›๐‘–๐‘›๐‘” ๐‘Ž๐‘™๐‘™ 3 ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘–๐‘œ๐‘›๐‘ : ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ + ๐Ÿ” ๐‘ฏ๐Ÿ๐‘ถ + 18 ๐ด๐‘‡๐‘ƒ + 12 [๐‘๐ด๐ท๐‘ƒ๐ป + ๐ป+] ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ + 18 [๐ด๐ท๐‘ƒ + ๐‘ƒ๐‘–] + 12 [๐‘๐ด๐ท๐‘ƒ+]
๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ (๐Ÿ๐Ÿ) ๐Ÿ ๐Ÿ ๐Ÿ“ ๐Ÿ‘ ๐‘ซ๐‘ฏ๐‘จ๐‘ท ๐Ÿ ๐Ÿ‘ ๐‘ญ๐’“๐’–๐’„. ๐Ÿ, ๐Ÿ” โˆ’๐’…๐’Š๐’‘๐’‰๐’๐’”. ๐‘ญ๐’“๐’–๐’„. ๐Ÿ” โˆ’ ๐‘ท (๐Ÿ‘) (๐Ÿ‘) ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ ๐Ÿ ๐Ÿ ๐‘ฟ๐’š๐’. ๐Ÿ“ โˆ’ ๐‘ท ๐‘ฌ๐’“๐’š. ๐Ÿ’ โˆ’ ๐‘ท (๐Ÿ) ๐‘บ๐’†๐’…. ๐Ÿ, ๐Ÿ• โˆ’ ๐’…๐’Š๐’‘. (๐Ÿ) ๐‘บ๐’†๐’…. ๐Ÿ• โˆ’ ๐‘ท (๐Ÿ) ๐‘น๐’Š๐’ƒ. ๐Ÿ“ โˆ’ ๐‘ท (๐Ÿ) (๐Ÿ’) ๐‘น๐’Š๐’ƒ๐’–. ๐Ÿ“ โˆ’ ๐‘ท (๐Ÿ”) ๐‘น๐’–๐‘ฉ๐‘ท ๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ (๐Ÿ”) ๐Ÿ, ๐Ÿ‘ โˆ’ ๐’…๐’Š๐‘ท๐‘ฎ๐‘จ (๐Ÿ๐Ÿ) (๐Ÿ๐Ÿ) โŸต ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ โŸถ ๐Ÿ‘๐‘ท๐’Š โŸถ ๐Ÿ๐‘ท๐’Š โŸถ ๐Ÿ” ๐‘จ๐‘ซ๐‘ท โŸต ๐Ÿ” ๐‘จ๐‘ป๐‘ท ๐Ÿ๐Ÿ ๐‘จ๐‘ป๐‘ท ๐Ÿ๐Ÿ ๐‘จ๐‘ซ๐‘ท โ†“ โ†‘ ๐Ÿ๐Ÿ [๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+] ๐Ÿ๐Ÿ ๐‘ต๐‘จ๐‘ซ๐‘ท+ โ†“ โ†‘ ๐Ÿ๐Ÿ ๐‘ท๐’Š โ†˜
๐‘จ๐’๐’‚๐’•๐’๐’Ž๐’š ๐’๐’‡ ๐‘ช๐Ÿ’ ๐’๐’†๐’‚๐’—๐’†๐’” 2 ๐‘ก๐‘ฆ๐‘๐‘’๐‘  ๐‘œ๐‘“ ๐‘๐‘’๐‘™๐‘™๐‘ /๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  ๐‘ด๐’†๐’”๐’๐’‘๐’‰๐’š๐’๐’ ๐‘ช๐’†๐’๐’๐’” ๐‘ฉ๐’–๐’๐’…๐’๐’† ๐‘บ๐’‰๐’†๐’‚๐’•๐’‰ ๐‘ช๐’†๐’๐’๐’” โ€ข ๐‘†๐‘š๐‘Ž๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘  โ€ข ๐ฟ๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘›๐‘œ. ๐‘œ๐‘“ ๐‘›๐‘œ๐‘Ÿ๐‘š๐‘Ž๐‘™ ๐‘ ๐‘–๐‘ง๐‘’ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘Ž ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘…๐‘ข๐ต๐‘–๐‘ ๐ถ๐‘‚ ๐‘Ž๐‘๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘œ๐‘๐‘๐‘ข๐‘Ÿ๐‘  โ€ข ๐ฟ๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘๐‘’๐‘™๐‘™๐‘  โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐‘“๐‘’๐‘ค ๐‘™๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘ ๐‘–๐‘ง๐‘’ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘Ž ๐‘Ž๐‘๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘…๐‘ข๐ต๐‘–๐‘ ๐ถ๐‘‚ ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐ท๐‘Ž๐‘Ÿ๐‘˜ ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘œ๐‘๐‘๐‘ข๐‘Ÿ๐‘ 
๐ถ๐‘‚2 ๐’Š ๐‘ช๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’•๐’Š๐’๐’ โˆถ ๐ป2๐ถ๐‘‚3 ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘›๐‘–๐‘ ๐‘Ž๐‘›โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘Ž๐‘ ๐‘’ โˆ’๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ = ๐‘‚๐‘ƒ๐‘‚3 2โˆ’ ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ + ๐ป2๐‘‚ ๐‘ช๐’‚๐’“๐’ƒ๐’๐’ ๐’…๐’Š๐’๐’™๐’Š๐’…๐’† ๐‘ช๐’‚๐’“๐’ƒ๐’๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘ท๐‘ฌ๐‘ท ๐‘ช๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’”๐’† ๐‘ท๐’Š ๐‘ฏ๐Ÿ๐‘ช๐‘ถ๐Ÿ‘
๐’Š๐’Š ๐‘น๐’†๐’…๐’–๐’„๐’•๐’Š๐’๐’ โˆถ ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐ป๐‘‚ โˆ’ ๐ถ๐ป โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ด๐’‚๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘€๐‘Ž๐‘™๐‘–๐‘ ๐ท๐‘’โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘”๐‘’๐‘›๐‘Ž๐‘ ๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘‡โ„Ž๐‘’ ๐‘š๐‘Ž๐‘™๐‘–๐‘ ๐‘Ž๐‘๐‘–๐‘‘ ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘ โ„Ž๐‘’๐‘Ÿ๐‘’ ๐‘–๐‘  ๐‘ ๐‘’๐‘›๐‘ก ๐‘ก๐‘œ ๐‘กโ„Ž๐‘’ ๐‘๐‘ข๐‘›๐‘‘๐‘™๐‘’ ๐‘ โ„Ž๐‘’๐‘Ž๐‘กโ„Ž ๐‘๐‘’๐‘™๐‘™๐‘ .
๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป3๐ถ โˆ’ ๐ป๐‘‚ โˆ’ ๐ถ๐ป โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ด๐’‚๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐’Š๐’Š๐’Š ๐‘ซ๐’†๐’„๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’•๐’Š๐’๐’ โˆถ ๐‘€๐‘Ž๐‘™๐‘–๐‘ ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† + ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’†
๐’Š๐’— ๐‘น๐’†๐’ˆ๐’†๐’๐’†๐’“๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ท๐‘ฌ๐‘ท: ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป3๐ถ โˆ’ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘‡โ„Ž๐‘’ ๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘–๐‘  ๐‘ ๐‘’๐‘›๐‘ก ๐‘๐‘Ž๐‘๐‘˜ ๐‘ก๐‘œ ๐‘š๐‘’๐‘ ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘๐‘œ๐‘›๐‘ฃ๐‘’๐‘Ÿ๐‘ ๐‘–๐‘œ๐‘› ๐‘–๐‘›๐‘ก๐‘œ ๐‘โ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘’๐‘›๐‘œ๐‘™ ๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’. โˆ’๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ = ๐‘‚๐‘ƒ๐‘‚3 2โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ƒ๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘‘๐‘–๐‘˜๐‘–๐‘›๐‘Ž๐‘ ๐‘’ ๐‘จ๐‘ซ๐‘ท ๐‘จ๐‘ป๐‘ท ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘’๐‘›๐‘œ๐‘™๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘๐‘Ž๐‘› ๐‘›๐‘œ๐‘ค ๐‘ก๐‘Ž๐‘˜๐‘’ ๐‘๐‘Ž๐‘Ÿ๐‘ก ๐‘–๐‘› ๐‘กโ„Ž๐‘’ ๐‘๐‘ฆ๐‘๐‘™๐‘’ ๐‘Ž๐‘”๐‘Ž๐‘–๐‘›.
๐‘ด๐’†๐’”๐’๐’‘๐’‰๐’š๐’๐’ ๐‘ช๐’†๐’๐’ ๐‘ฉ๐’–๐’๐’…๐’๐’† ๐‘บ๐’‰๐’†๐’‚๐’•๐’‰ ๐‘ช๐’†๐’๐’ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ท๐‘ฌ๐‘ท ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’‚๐’•๐’† ๐‘จ๐‘ซ๐‘ท โŸต ๐‘จ๐‘ป๐‘ท โŸถ โŸต ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ท๐’Š ๐‘ช๐‘ถ๐Ÿ + ๐‘ฏ๐Ÿ๐‘ถ ๐‘ฏ๐Ÿ๐‘ช๐‘ถ๐Ÿ‘ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ด๐’‚๐’๐’‚๐’•๐’† โŸต ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’๐’‚๐’”๐’• ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’๐’‚๐’”๐’• ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’† ๐‘ฎ๐’๐’–๐’„๐’๐’”๐’†
๐ด๐‘ก ๐‘›๐‘–๐‘”โ„Ž๐‘ก, ๐‘กโ„Ž๐‘’ ๐‘ ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘Ž ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘œ๐‘๐‘’๐‘› ๐‘Ž๐‘™๐‘™๐‘œ๐‘ค๐‘–๐‘›๐‘” ๐ถ๐‘‚2 ๐‘ก๐‘œ ๐‘‘๐‘–๐‘“๐‘“๐‘ข๐‘ ๐‘’ ๐‘–๐‘›๐‘ก๐‘œ ๐‘กโ„Ž๐‘’ ๐‘š๐‘’๐‘ ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘ช๐‘ถ๐Ÿ ๐‘ฏ๐‘ช๐‘ถ๐Ÿ‘ โˆ’ + ๐‘ถ๐‘ฏ โˆ’ [๐‘ฉ๐’Š๐’„๐’‚๐’“๐’ƒ๐’๐’๐’‚๐’•๐’†] ๐‘ท๐‘ฌ๐‘ท ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ฏ๐‘ช๐‘ถ๐Ÿ‘ โˆ’ ๐‘ฏ๐Ÿ‘๐‘ท๐‘ถ๐Ÿ’ ๐‘ถ๐‘จ๐‘จ ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’‚๐’•๐’† ๐‘ถ๐‘จ๐‘จ ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘€๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐ท๐‘’โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘”๐‘’๐‘›๐‘Ž๐‘ ๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ƒ๐ธ๐‘ƒ ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘ฅ๐‘ฆ๐‘™๐‘Ž๐‘ ๐‘’
๐‘‡โ„Ž๐‘’ ๐‘š๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’๐‘‘ ๐‘–๐‘  ๐‘ ๐‘ก๐‘œ๐‘Ÿ๐‘’๐‘‘ ๐‘–๐‘› ๐‘กโ„Ž๐‘’ ๐‘ฃ๐‘Ž๐‘๐‘ข๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘‡โ„Ž๐‘’ ๐‘Ž๐‘๐‘๐‘ข๐‘š๐‘ข๐‘™๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ ๐‘œ๐‘Ÿ๐‘”๐‘Ž๐‘›๐‘–๐‘ ๐‘Ž๐‘๐‘–๐‘‘๐‘  ๐‘๐‘Ž๐‘ข๐‘ ๐‘’๐‘  ๐‘กโ„Ž๐‘’ ๐‘Ž๐‘๐‘–๐‘‘๐‘–๐‘“๐‘–๐‘๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† + ๐‘ช๐‘ถ๐Ÿ ๐‘€๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’† ๐ท๐‘ข๐‘Ÿ๐‘–๐‘›๐‘” ๐‘‘๐‘Ž๐‘ฆ๐‘ก๐‘–๐‘š๐‘’, ๐‘กโ„Ž๐‘’ ๐‘ ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘Ž ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘๐‘™๐‘œ๐‘ ๐‘’ & ๐‘๐‘Ÿ๐‘’๐‘ฃ๐‘’๐‘›๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘ ๐‘ ๐‘–๐‘ฃ๐‘’ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘™๐‘œ๐‘ ๐‘ . ๐‘‡โ„Ž๐‘’ ๐ถ๐‘‚2 ๐‘™๐‘–๐‘๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘’๐‘›๐‘ก๐‘’๐‘Ÿ๐‘  ๐ถ3 ๐ถ๐‘ฆ๐‘๐‘™๐‘’ ๐‘“๐‘œ๐‘Ÿ ๐‘๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘› โˆ’ ๐‘“๐‘–๐‘ฅ๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘ข๐‘ ๐‘–๐‘›๐‘” ๐‘กโ„Ž๐‘’ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘–๐‘œ๐‘›.
Photosynthesis

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Photosynthesis

  • 1. ๐Ÿ”๐‘ช๐‘ถ๐Ÿ + ๐Ÿ๐Ÿ๐‘ฏ๐Ÿ๐‘ถ ๐‘ช๐Ÿ”๐‘ฏ๐Ÿ๐Ÿ๐‘ถ๐Ÿ” + ๐Ÿ”๐‘ฏ๐Ÿ๐‘ถ + ๐Ÿ”๐‘ถ๐Ÿ โ†‘ ๐‘†๐‘ข๐‘›๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™
  • 2.
  • 3. โ€ข 2 โˆ’ ๐‘™๐‘Ž๐‘ฆ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘’ ๐‘๐‘œ๐‘›๐‘ ๐‘–๐‘ ๐‘ก๐‘–๐‘›๐‘” ๐‘œ๐‘“ ๐’๐’–๐’•๐’†๐’“ & ๐’Š๐’๐’๐’†๐’“ ๐’Ž๐’†๐’Ž๐’ƒ๐’“๐’‚๐’๐’†๐’”. โ€ข ๐ต๐‘œ๐‘กโ„Ž ๐‘ ๐‘’๐‘๐‘Ž๐‘Ÿ๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘Ž ๐‘“๐‘™๐‘ข๐‘–๐‘‘ ๐‘“๐‘–๐‘™๐‘™๐‘’๐‘‘ ๐‘ ๐‘๐‘Ž๐‘๐‘’ 100 โˆ’ 200 โ„ซ ๐‘–. ๐‘’. ๐’‘๐’†๐’“๐’Š โˆ’ ๐’‘๐’๐’‚๐’”๐’•๐’Š๐’…๐’Š๐’‚๐’ ๐’”๐’‘๐’‚๐’„๐’†. โ€ข ๐ฟ๐‘–๐‘ž๐‘ข๐‘–๐‘‘, ๐‘๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘Ž๐‘๐‘’๐‘œ๐‘ข๐‘  ๐‘š๐‘Ž๐‘ก๐‘Ÿ๐‘–๐‘ฅ โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘Ž๐‘Ÿ; ๐‘๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘›๐‘–๐‘›๐‘” ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’๐‘  โ€ข ๐‘บ๐’Š๐’•๐’† ๐’๐’‡ ๐‘ซ๐’‚๐’“๐’Œ ๐’“๐’†๐’‚๐’„๐’•๐’Š๐’๐’ ๐‘œ๐‘“ ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ ๐‘–๐‘  โ€ข ๐ถ๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘›๐‘  ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก ๐‘ซ๐‘ต๐‘จ, ๐‘ ๐‘ก๐‘Ž๐‘Ÿ๐‘โ„Ž ๐‘”๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘’๐‘ , ๐Ÿ•๐ŸŽ ๐‘บ ๐’“๐’Š๐’ƒ๐’๐’”๐’๐’Ž๐’†๐’”, ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘ .
  • 4. โ€ข ๐‘‡โ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ โŸน ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘œ๐‘ข๐‘  ๐‘ ๐‘Ž๐‘๐‘˜; ๐’„๐’๐’๐’•๐’‚๐’Š๐’ ๐’‘๐’Š๐’ˆ๐’Ž๐’†๐’๐’•๐’” โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘š โŸน ๐‘ ๐‘ก๐‘Ž๐‘๐‘˜ ๐‘œ๐‘“ ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐‘บ๐’Š๐’•๐’† ๐’๐’‡ ๐‘ณ๐’Š๐’ˆ๐’‰๐’• ๐’“๐’†๐’‚๐’„๐’•๐’Š๐’๐’ ๐‘œ๐‘“ ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ ๐‘–๐‘  โ€ข ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ โŸน ๐‘๐‘œ๐‘›๐‘›๐‘’๐‘๐‘ก ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘๐‘ 
  • 5. ๐‘‚๐‘ข๐‘ก๐‘’๐‘Ÿ ๐‘š๐‘’๐‘š๐‘. ๐ผ๐‘›๐‘›๐‘’๐‘Ÿ ๐‘š๐‘’๐‘š๐‘. ๐‘ƒ๐‘’๐‘Ÿ๐‘–๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘–๐‘‘๐‘–๐‘Ž๐‘™ ๐‘ ๐‘๐‘Ž๐‘๐‘’ ๐ท๐‘๐ด ๐‘…๐‘–๐‘๐‘œ๐‘ ๐‘œ๐‘š๐‘’ ๐‘†๐‘ก๐‘Ž๐‘Ÿ๐‘โ„Ž ๐‘”๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘™๐‘’ ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ ๐‘‡โ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘ข๐‘š ๐‘บ๐‘ป๐‘น๐‘ผ๐‘ช๐‘ป๐‘ผ๐‘น๐‘ฌ ๐‘ถ๐‘ญ ๐‘ช๐‘ฏ๐‘ณ๐‘ถ๐‘น๐‘ถ๐‘ท๐‘ณ๐‘จ๐‘บ๐‘ป
  • 6. โ€ข ๐บ๐‘Ÿ๐‘’๐‘’๐‘˜: ๐’„๐’‰๐’๐’๐’“๐’๐’” = ๐’ˆ๐’“๐’†๐’†๐’ ; ๐’‘๐’‰๐’š๐’๐’๐’๐’ = ๐’๐’†๐’‚๐’‡ โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ , ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘๐‘ฆ๐‘Ž๐‘›๐‘œ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž โ€ข ๐น๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐’‘๐’“๐’๐’•๐’๐’„๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’ ๐‘–๐‘› ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘๐‘’ ๐‘œ๐‘“ ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐‘จ๐’ƒ๐’”๐’๐’“๐’ƒ๐’” โŸน ๐‘น๐‘ฌ๐‘ซ & ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ ๐’๐’Š๐’ˆ๐’‰๐’• โ€ข ๐‘น๐’†๐’‡๐’๐’†๐’„๐’•๐’” โŸน ๐‘ฎ๐‘น๐‘ฌ๐‘ฌ๐‘ต ๐’๐’Š๐’ˆ๐’‰๐’• ; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘™๐‘’๐‘Ž๐‘ฃ๐‘’๐‘  ๐‘Ž๐‘๐‘๐‘’๐‘Ž๐‘Ÿ ๐‘”๐‘Ÿ๐‘’๐‘’๐‘› ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ. โ€ข ๐‘‡๐‘ฆ๐‘๐‘’๐‘  ๐‘œ๐‘“ ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™: ๐‘– ๐ผ๐‘› โ„Ž๐‘–๐‘”โ„Ž๐‘’๐‘Ÿ ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ : ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’๐’” ๐’‚ & ๐’ƒ ๐‘–๐‘– ๐ผ๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’: ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’๐’” ๐’„, ๐’…, ๐’† ๐‘–๐‘–๐‘– ๐ผ๐‘› ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž: ๐‘ฉ๐’‚๐’„๐’•๐’†๐’“๐’Š๐’ โˆ’ ๐’„๐’‰๐’๐’๐’“๐’๐’‘๐’‰๐’š๐’๐’ & ๐’ƒ๐’‚๐’„๐’•๐’†๐’“๐’Š๐’ โˆ’ ๐’—๐’Š๐’“๐’Š๐’…๐’Š๐’
  • 7. โ€ข ๐‘‡๐‘Ž๐‘‘๐‘๐‘œ๐‘™๐‘’ โˆ’ ๐‘ โ„Ž๐‘Ž๐‘๐‘’๐‘‘ ๐‘ ๐‘ก๐‘Ÿ๐‘ข๐‘๐‘ก๐‘ข๐‘Ÿ๐‘’ โ€ข ๐‘ท๐’๐’“๐’‘๐’‰๐’š๐’“๐’Š๐’ ๐’‰๐’†๐’‚๐’… โŸถ 4 ๐‘๐‘ฆ๐‘Ÿ๐‘Ÿ๐‘œ๐‘™๐‘’ ๐‘Ÿ๐‘–๐‘›๐‘”๐‘  ๐‘ค๐‘–๐‘กโ„Ž 4 ๐‘ โˆ’ ๐‘Ž๐‘ก๐‘œ๐‘š๐‘  ๐‘กโ„Ž๐‘Ž๐‘ก ๐‘ ๐‘ข๐‘Ÿ๐‘Ÿ๐‘œ๐‘ข๐‘›๐‘‘ ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘Ž๐‘™ ๐‘€๐‘” โˆ’ ๐‘Ž๐‘ก๐‘œ๐‘š. โ€ข ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐’•๐’‚๐’Š๐’ โŸถ ๐‘™๐‘œ๐‘›๐‘” โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘› ๐‘โ„Ž๐‘Ž๐‘–๐‘› โ€ข ๐ป๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘โ„Ž๐‘–๐‘™๐‘–๐‘ ๐ป๐‘’๐‘Ž๐‘‘ โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐ป๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘โ„Ž๐‘œ๐‘๐‘–๐‘ ๐‘ก๐‘Ž๐‘–๐‘™ โŸน ๐ด๐‘›๐‘โ„Ž๐‘œ๐‘Ÿ๐‘  ๐‘ก๐‘œ ๐‘กโ„Ž๐‘ฆ๐‘™๐‘Ž๐‘˜๐‘œ๐‘–๐‘‘ ๐‘š๐‘’๐‘š๐‘๐‘Ÿ๐‘Ž๐‘›๐‘’ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”๐‘กโ„Ž๐‘  ๐‘œ๐‘“ ๐’—๐’Š๐’๐’๐’†๐’• โˆ’ ๐’ƒ๐’๐’–๐’† & ๐’๐’“๐’‚๐’๐’ˆ๐’† โˆ’ ๐’“๐’†๐’… ๐‘™๐‘–๐‘”โ„Ž๐‘ก. โ€ข ๐‘ƒ๐‘Ÿ๐‘–๐‘š๐‘Ž๐‘Ÿ๐‘ฆ ๐‘’๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘› ๐‘‘๐‘œ๐‘›๐‘œ๐‘Ÿ โ€ข ๐บ๐‘–๐‘ฃ๐‘’๐‘  ๐’ˆ๐’“๐’†๐’†๐’ ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘ก๐‘œ ๐’๐’†๐’‚๐’—๐’†๐’”
  • 8. ๐ถ๐ป2๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป3 ๐ถ๐ป2 = ๐ถ๐ป ๐ถ๐ป3 ๐‘‚ ๐ถ๐ป3 ๐‘–๐‘› ๐ถโ„Ž๐‘™. ๐‘Ž & ๐ถ๐ป๐‘‚ ๐‘–๐‘› ๐ถโ„Ž๐‘™. ๐‘ ๐‘ต ๐‘ต ๐‘ต ๐‘ต โŠ– โŠ– ๐‘ด๐’ˆ ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐‘ท๐’๐’“๐’‘๐’‰๐’š๐’“๐’Š๐’ ๐‘ฏ๐’†๐’‚๐’… ๐‘ท๐’‰๐’š๐’•๐’๐’ ๐‘ป๐’‚๐’Š๐’ ๐‘‚ ๐‘‚ ๐ป2๐ถ ๐‘ฏ๐’†๐’‚๐’…
  • 9. โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘๐‘™๐‘Ž๐‘›๐‘ก๐‘ , ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘โ„Ž๐‘œ๐‘ก๐‘œ๐‘ ๐‘ฆ๐‘›๐‘กโ„Ž๐‘’๐‘ก๐‘–๐‘ ๐‘๐‘Ž๐‘๐‘ก๐‘’๐‘Ÿ๐‘–๐‘Ž โ€ข ๐ต๐‘Ÿ๐‘–๐‘”โ„Ž๐‘ก ๐’“๐’†๐’…, ๐’š๐’†๐’๐’๐’๐’˜ ๐’๐’“ ๐’๐’“๐’‚๐’๐’ˆ๐’† ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ โ€ข ๐ด๐‘๐‘๐‘’๐‘ ๐‘ ๐‘œ๐‘Ÿ๐‘ฆ ๐‘๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘กโ„Ž๐‘’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘›๐‘œ๐‘ก ๐‘Ž๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘ญ๐‘ผ๐‘ต๐‘ช๐‘ป๐‘ฐ๐‘ถ๐‘ต๐‘บ: ๐‘– ๐‘จ๐’ƒ๐’”๐’๐’“๐’‘๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ ๐’๐’Š๐’ˆ๐’‰๐’• ๐‘–๐‘– ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘ ๐‘“๐‘’๐‘Ÿ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ก๐‘œ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘–๐‘–๐‘– ๐‘ƒ๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘๐‘ก ๐‘“๐‘Ÿ๐‘œ๐‘š ๐‘œ๐‘ฅ๐‘–๐‘‘๐‘Ž๐‘ก๐‘–๐‘œ๐‘› & ๐‘’๐‘ฅ๐‘๐‘’๐‘ ๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘ฃ ๐‘‰๐‘–๐‘ก๐‘Ž๐‘š๐‘–๐‘› ๐ด ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก๐‘–๐‘œ๐‘› ๐‘ฃ ๐บ๐‘–๐‘ฃ๐‘’ ๐’„๐’๐’๐’๐’–๐’“ ๐’•๐’ ๐’‡๐’๐’๐’˜๐’†๐’“๐’” & ๐’‡๐’“๐’–๐’Š๐’•๐’”
  • 10. ๐‘ป๐’€๐‘ท๐‘ฌ๐‘บ: 1) ๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’๐‘ : 2) ๐‘‹๐‘Ž๐‘›๐‘กโ„Ž๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  (๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘™๐‘ ): โ€ข ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’† โˆ’ ๐‘น๐’†๐’… ๐‘–๐‘› ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ผ๐‘ฝ, ๐‘ฝ๐’Š๐’๐’๐’†๐’• & ๐‘ฉ๐’๐’–๐’† ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐‘†๐‘๐‘Ž๐‘ก๐‘ก๐‘’๐‘Ÿ ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’†, ๐‘น๐’†๐’… & ๐’€๐’†๐’๐’๐’๐’˜ ๐‘™๐‘–๐‘”โ„Ž๐‘ก โ€ข ๐บ๐‘’๐‘›. ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘ข๐‘™๐‘Ž = ๐ถ40๐ป56 โ€ข ๐ธ๐‘ฅ. ๐‘ณ๐’š๐’„๐’๐’‘๐’†๐’๐’†๐’” ๐‘…๐‘’๐‘‘ ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘–๐‘› ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘œ & ๐‘โ„Ž๐‘–๐‘™๐‘™๐‘– , ๐›ผ โˆ’ ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’ & ๐›ฝ โˆ’ ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘’. โ€ข ๐ถ๐‘œ๐‘›๐‘ก๐‘Ž๐‘–๐‘› ๐‘œ๐‘ฅ๐‘ฆ๐‘”๐‘’๐‘› โ€ข ๐บ๐‘’๐‘›. ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘ข๐‘™๐‘Ž = ๐ถ40๐ป56๐‘‚ โ€ข ๐ธ๐‘ฅ. ๐ถ๐‘Ÿ๐‘ฆ๐‘๐‘ก๐‘œ๐‘ฅ๐‘Ž๐‘›๐‘กโ„Ž๐‘–๐‘›, ๐‘ณ๐’–๐’•๐’†๐’Š๐’ (๐‘ฆ๐‘’๐‘™๐‘™๐‘œ๐‘ค๐‘–๐‘ โ„Ž ๐‘๐‘œ๐‘™๐‘œ๐‘ข๐‘Ÿ ๐‘œ๐‘“ ๐‘Ž๐‘ข๐‘ก๐‘ข๐‘š๐‘›๐‘Ž๐‘™ ๐‘“๐‘œ๐‘™๐‘–๐‘Ž๐‘”๐‘’), ๐‘ญ๐’–๐’„๐’๐’™๐’‚๐’๐’•๐’‰๐’Š๐’ (๐ต๐‘Ÿ๐‘œ๐‘ค๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’)
  • 11. โ€ข ๐บ๐‘Ÿ๐‘’๐‘’๐‘˜: ๐’‘๐’‰๐’š๐’Œ๐’๐’” = ๐’‚๐’๐’ˆ๐’‚ ; ๐’ƒ๐’Š๐’๐’Š๐’” = ๐’ƒ๐’Š๐’๐’† โ€ข ๐‘‚๐‘๐‘๐‘ข๐‘Ÿ๐‘  ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ & ๐‘๐‘™๐‘ข๐‘’ โˆ’ ๐‘”๐‘Ÿ๐‘’๐‘’๐‘› ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’ โ€ข ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘กโ„Ž๐‘’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘›๐‘œ๐‘ก ๐‘Ž๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘’๐‘‘ ๐‘๐‘ฆ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  & ๐‘๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐‘Š๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘ ๐‘œ๐‘™๐‘ข๐‘๐‘™๐‘’ โ€ข ๐‘ป๐’€๐‘ท๐‘ฌ๐‘บ โˆ’ ๐‘– ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘’๐‘Ÿ๐‘ฆ๐‘กโ„Ž๐‘Ÿ๐‘–๐‘› (๐‘น๐‘ฌ๐‘ซ): โŸน ๐‘“๐‘œ๐‘ข๐‘›๐‘‘ ๐‘–๐‘› ๐‘…โ„Ž๐‘œ๐‘‘๐‘œ๐‘โ„Ž๐‘ฆ๐‘ก๐‘Ž (๐‘…๐‘’๐‘‘ ๐‘Ž๐‘™๐‘”๐‘Ž๐‘’) โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ฉ๐’๐’–๐’† & ๐‘ฎ๐’“๐’†๐’†๐’ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘–๐‘– ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘๐‘ฆ๐‘Ž๐‘›๐‘–๐‘› ๐‘ฉ๐‘ณ๐‘ผ๐‘ฌ : โŸน ๐‘“๐‘œ๐‘ข๐‘›๐‘‘ ๐‘–๐‘› ๐ถ๐‘ฆ๐‘Ž๐‘›๐‘œ๐‘โ„Ž๐‘ฆ๐‘ก๐‘Ž (๐ต๐บ๐ด) โŸน ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘ ๐‘ถ๐’“๐’‚๐’๐’ˆ๐’† & ๐‘น๐’†๐’… ๐‘™๐‘–๐‘”โ„Ž๐‘ก
  • 13.
  • 14. ๐‘š๐‘Ž๐‘‘๐‘’ ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘ , ๐‘๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  & ๐‘๐‘œ โˆ’ ๐‘“๐‘Ž๐‘๐‘ก๐‘œ๐‘Ÿ๐‘  ๐‘†๐‘–๐‘ก๐‘’ ๐‘œ๐‘“ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘› ๐‘ƒ๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’ ๐ด๐‘‡๐‘ƒ & ๐‘๐ด๐ท๐‘ƒ๐ป ๐ถ๐‘Ž๐‘๐‘ก๐‘ข๐‘Ÿ๐‘’ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘ƒ๐‘Ÿ๐‘œ๐‘š๐‘œ๐‘ก๐‘’ ๐‘’โˆ’ ๐‘ก๐‘œ โ†‘ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ ๐‘ก๐‘Ž๐‘ก๐‘’ ๐‘ƒ๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘–๐‘›๐‘  & ๐ถโ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘  ๐‘†๐‘ข๐‘Ÿ๐‘Ÿ๐‘œ๐‘ข๐‘›๐‘‘ ๐‘กโ„Ž๐‘’ ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘ ๐‘“๐‘’๐‘Ÿ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘ก๐‘œ ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’
  • 15. โ€ข ๐ท๐‘–๐‘ ๐‘๐‘œ๐‘ฃ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘๐‘’๐‘“๐‘œ๐‘Ÿ๐‘’; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐‘ท๐‘บ ๐‘ฐ. โ€ข ๐ฟ๐‘œ๐‘๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘œ๐‘›: ๐‘– ๐‘ถ๐’–๐’•๐’†๐’“ ๐’”๐’–๐’“๐’‡๐’‚๐’„๐’† ๐’๐’‡ ๐’•๐’‰๐’š๐’๐’‚๐’Œ๐’๐’Š๐’… ๐’Ž๐’†๐’Ž๐’ƒ. ๐‘–๐‘– ๐‘†๐‘ก๐‘Ÿ๐‘œ๐‘š๐‘Ž ๐‘™๐‘Ž๐‘š๐‘’๐‘™๐‘™๐‘Ž๐‘’ โ€ข ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ โŸน ๐‘ช๐’‰๐’. ๐’‚ ๐’Ž๐’๐’๐’†๐’„๐’–๐’๐’† ๐‘ท โˆ’ ๐Ÿ•๐ŸŽ๐ŸŽ ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ & ๐‘“๐‘Ž๐‘Ÿ ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ž๐‘ก 700 ๐‘›๐‘š ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”โ„Ž๐‘ก โ€ข ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐ป๐‘Ž๐‘Ÿ๐‘ฃ. ๐ถ๐‘œ๐‘š๐‘๐‘™๐‘’๐‘ฅ โŸน ๐ถโ„Ž๐‘™. ๐‘ + ๐ถโ„Ž๐‘™. ๐‘Ž 670, 680, 695 + ๐ถ๐‘Ž๐‘Ÿ๐‘œ๐‘ก๐‘’๐‘›๐‘œ๐‘–๐‘‘๐‘  โ€ข ๐’†โˆ’ ๐’…๐’๐’๐’๐’“ โŸน ๐‘ƒ๐‘™๐‘Ž๐‘ ๐‘ก๐‘œ๐‘๐‘ฆ๐‘Ž๐‘›๐‘–๐‘› โ€ข ๐’†โˆ’ ๐’‚๐’„๐’„๐’†๐’‘๐’•๐’๐’“ โŸน ๐ผ๐‘Ÿ๐‘œ๐‘› โˆ’ ๐‘ ๐‘ข๐‘™๐‘โ„Ž๐‘ข๐‘Ÿ ๐น๐‘’๐‘† ๐‘๐‘’๐‘›๐‘ก๐‘’๐‘Ÿ๐‘ 
  • 16. โ€ข ๐ด๐‘๐‘ก๐‘  ๐‘“๐‘–๐‘Ÿ๐‘ ๐‘ก, ๐‘๐‘ข๐‘ก ๐‘‘๐‘–๐‘ ๐‘๐‘œ๐‘ฃ๐‘’๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘Ž๐‘ก๐‘’๐‘Ÿ; โ„Ž๐‘’๐‘›๐‘๐‘’ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐‘ท๐‘บ ๐‘ฐ๐‘ฐ. โ€ข ๐ฟ๐‘œ๐‘๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘œ๐‘›: ๐‘ฐ๐’๐’๐’†๐’“ ๐’”๐’–๐’“๐’‡๐’‚๐’„๐’† ๐’๐’‡ ๐’•๐’‰๐’š๐’๐’‚๐’Œ๐’๐’Š๐’… ๐’Ž๐’†๐’Ž๐’ƒ. โ€ข ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘๐‘’๐‘›๐‘ก๐‘Ÿ๐‘’ โŸน ๐‘ช๐’‰๐’. ๐’‚ ๐’Ž๐’๐’๐’†๐’„๐’–๐’๐’† ๐‘ท โˆ’ ๐Ÿ”๐Ÿ–๐ŸŽ ๐ด๐‘๐‘ก๐‘–๐‘ฃ๐‘’ ๐‘–๐‘› ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก, ๐‘›๐‘œ๐‘ก ๐‘–๐‘› ๐‘“๐‘Ž๐‘Ÿ ๐‘Ÿ๐‘’๐‘‘ ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐ด๐‘๐‘ ๐‘œ๐‘Ÿ๐‘๐‘  ๐‘™๐‘–๐‘”โ„Ž๐‘ก ๐‘Ž๐‘ก 680 ๐‘›๐‘š ๐‘ค๐‘Ž๐‘ฃ๐‘’๐‘™๐‘’๐‘›๐‘”โ„Ž๐‘ก โ€ข ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐ป๐‘Ž๐‘Ÿ๐‘ฃ. ๐ถ๐‘œ๐‘š๐‘๐‘™๐‘’๐‘ฅ โŸน ๐ถโ„Ž๐‘™. ๐‘Ž 660, 670, 680, 695, 700 + ๐ถโ„Ž๐‘™. ๐‘ + ๐‘ƒโ„Ž๐‘ฆ๐‘๐‘œ๐‘๐‘–๐‘™๐‘–๐‘›๐‘  + ๐‘‹๐‘Ž๐‘›๐‘กโ„Ž๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™๐‘  โ€ข ๐’†โˆ’ ๐’…๐’๐’๐’๐’“ โŸน ๐‘Š๐‘Ž๐‘ก๐‘’๐‘Ÿ โ€ข ๐’†โˆ’ ๐’‚๐’„๐’„๐’†๐’‘๐’•๐’๐’“ โŸน ๐‘ƒ๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘ , ๐‘ž๐‘ข๐‘–๐‘›๐‘œ๐‘›๐‘’
  • 17.
  • 18. ๐ด๐‘๐‘๐‘’๐‘ ๐‘ ๐‘œ๐‘Ÿ๐‘ฆ ๐‘ƒ๐‘–๐‘”๐‘š๐‘’๐‘›๐‘ก๐‘  ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘ณ๐’Š๐’ˆ๐’‰๐’• ๐’‚๐’ƒ๐’”๐’๐’“๐’‘๐’•๐’Š๐’๐’ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘ฌ๐’๐’†๐’“๐’ˆ๐’š ๐’•๐’“๐’‚๐’๐’”๐’‡๐’†๐’“ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘: ๐‘ฌ๐’™๐’„๐’Š๐’•๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ช๐’‰๐’. ๐’‚ ๐‘ฏ๐Ÿ๐‘ถ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ’: ๐‘ท๐’‰๐’๐’•๐’๐’๐’š๐’”๐’Š๐’” ๐’๐’‡ ๐’˜๐’‚๐’•๐’†๐’“ ๐‘ถ๐Ÿ + - - ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“: ๐‘ญ๐’๐’“๐’Ž. ๐’๐’‡ ๐’‚๐’”๐’”๐’Š๐’Ž๐’Š๐’๐’Š๐’•๐’‚๐’“๐’š ๐’‘๐’๐’˜๐’†๐’“ ๐‘จ๐‘ซ๐‘ท + ๐‘ท๐’Š โŸถ ๐‘จ๐‘ป๐‘ท ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ
  • 19. โ€ข ๐‘ƒโ„Ž๐‘œ๐‘ก๐‘œ๐‘™๐‘ฆ๐‘ ๐‘–๐‘  ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ & ๐‘‚2 ๐‘’๐‘ฃ๐‘œ๐‘™๐‘ข๐‘ก๐‘–๐‘œ๐‘› ๐‘‘๐‘œ๐‘’๐‘  ๐‘›๐‘œ๐‘ก ๐‘ก๐‘Ž๐‘˜๐‘’ ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐‘๐ด๐ท๐‘ƒ๐ป ๐‘–๐‘  ๐‘›๐‘œ๐‘ก ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘. โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐‘ƒ๐‘† โˆ’ ๐ผ ๐‘–๐‘  ๐‘–๐‘›๐‘ฃ๐‘œ๐‘™๐‘ฃ๐‘’๐‘‘. โ€ข ๐ด๐‘‡๐‘ƒ ๐‘–๐‘  ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’๐‘‘ ๐‘Ž๐‘ก 2 ๐‘ ๐‘–๐‘ก๐‘’๐‘ . โ€ข ๐ธ๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘  ๐‘Ÿ๐‘’๐‘ก๐‘ข๐‘Ÿ๐‘› ๐‘๐‘Ž๐‘๐‘˜ ๐‘ก๐‘œ ๐‘ƒ๐‘† โˆ’ ๐ผ.
  • 20. ๐‘ช๐’€๐‘ช๐‘ณ๐‘ฐ๐‘ช ๐‘ท๐’‰๐’๐’•๐’๐’ ๐น๐‘’๐‘Ÿ๐‘Ÿ๐‘–๐‘‘๐‘œ๐‘ฅ๐‘–๐‘› ๐‘…๐‘’๐‘‘๐‘ข๐‘๐‘–๐‘›๐‘” ๐‘†๐‘ข๐‘๐‘ ๐‘ก๐‘Ž๐‘›๐‘๐‘’ ๐‘ท๐’‰๐’๐’•๐’๐’๐’” โ†–โ†–โ†– ๐‘ญ๐’†๐’“๐’“๐’Š๐’…๐’๐’™๐’Š๐’ ๐‘ท๐’๐’‚๐’”๐’•๐’๐’„๐’š๐’‚๐’๐’Š๐’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐Ÿ๐’†โˆ’ ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘ท๐‘บ โˆ’ ๐‘ฐ (๐‘ท๐Ÿ•๐ŸŽ๐ŸŽ)
  • 21. โ€ข ๐‘ƒโ„Ž๐‘œ๐‘ก๐‘œ๐‘™๐‘ฆ๐‘ ๐‘–๐‘  ๐‘œ๐‘“ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ & ๐‘‚2 ๐‘’๐‘ฃ๐‘œ๐‘™๐‘ข๐‘ก๐‘–๐‘œ๐‘› ๐‘ก๐‘Ž๐‘˜๐‘’๐‘  ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐‘๐ด๐ท๐‘ƒ๐ป ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘ก๐‘Ž๐‘˜๐‘’๐‘  ๐‘๐‘™๐‘Ž๐‘๐‘’. โ€ข ๐ต๐‘œ๐‘กโ„Ž ๐‘ƒ๐‘† โˆ’ ๐ผ & ๐‘ƒ๐‘† โˆ’ ๐ผ๐ผ ๐‘Ž๐‘Ÿ๐‘’ ๐‘–๐‘›๐‘ฃ๐‘œ๐‘™๐‘ฃ๐‘’๐‘‘. โ€ข ๐ผ๐‘ก ๐‘–๐‘  ๐‘Ž๐‘™๐‘ ๐‘œ ๐‘๐‘Ž๐‘™๐‘™๐‘’๐‘‘ ๐’ โˆ’ ๐’”๐’„๐’‰๐’†๐’Ž๐’† ๐‘‘๐‘ข๐‘’ ๐‘ก๐‘œ ๐‘–๐‘ก๐‘  ๐‘ง๐‘–๐‘” โˆ’ ๐‘ง๐‘Ž๐‘” ๐‘Ÿ๐‘œ๐‘ข๐‘ก๐‘’ ๐‘œ๐‘“ ๐‘’๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘ . โ€ข ๐ธ๐‘™๐‘’๐‘๐‘ก๐‘Ÿ๐‘œ๐‘›๐‘  ๐‘‘๐‘œ ๐‘›๐‘œ๐‘ก ๐‘Ÿ๐‘’๐‘ก๐‘ข๐‘Ÿ๐‘› ๐‘ก๐‘œ ๐‘ƒ๐‘† โˆ’ ๐ผ ๐‘œ๐‘Ÿ ๐‘ƒ๐‘† โˆ’ ๐ผ๐ผ.
  • 22. ๐‘ท๐’‰๐’๐’•๐’๐’๐’” โ†–โ†– ๐‘ญ๐’†๐’“๐’“๐’Š๐’…๐’๐’™๐’Š๐’ ๐‘ท๐’๐’‚๐’”๐’•๐’๐’’๐’–๐’Š๐’๐’๐’๐’† ๐Ÿ’๐’†โˆ’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘จ๐‘ซ๐‘ท ๐‘ท๐’Š ๐‘ท๐‘บ โˆ’ ๐‘ฐ๐‘ฐ (๐‘ท๐Ÿ”๐Ÿ–๐ŸŽ) ๐‘ท๐‘บ โˆ’ ๐‘ฐ (๐‘ท๐Ÿ•๐ŸŽ๐ŸŽ) โ†—โ†— ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’ ๐‘ฏ๐Ÿ๐‘ถ ๐Ÿ’ ร— ๐Ÿ’๐‘ฏ+ ๐Ÿ๐‘ฏ๐Ÿ๐‘ถ ๐Ÿ’๐’†โˆ’ ๐Ÿ’๐’†โˆ’
  • 23.
  • 24. ๐Ÿ‘ ๐‘ท๐’‰๐’‚๐’”๐’†๐’” ๐‘ญ๐’Š๐’™๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’๐’๐’—๐’†๐’“๐’”๐’Š๐’๐’ ๐’๐’‡ ๐‘ท๐‘ฎ๐‘จ ๐’•๐’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ ๐‘น๐’†๐’ˆ๐’†๐’๐’†๐’“๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘น๐’–๐‘ฉ๐‘ท
  • 25. ๐ถ = ๐‘‚ ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐Ÿ’ ๐Ÿ“ ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ“ โˆ’ ๐’ƒ๐’Š๐’”๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† (๐‘น๐’–๐‘ฉ๐‘ท) 6 ร— ๐‘น๐’–๐‘ฉ๐’Š๐’”๐‘ช๐‘ถ ๐ป๐ถ โˆ’ ๐‘‚๐ป ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ 12 ร— ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ) [๐Ÿ” ร— ๐Ÿ“ ๐‘ช = ๐Ÿ‘๐ŸŽ ๐‘ช] [๐Ÿ๐Ÿ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ‘๐Ÿ” ๐‘ช] + ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ + ๐Ÿ” ๐‘ฏ๐Ÿ๐‘ถ ๐‘…๐‘–๐‘๐‘ข๐‘™๐‘œ๐‘ ๐‘’ ๐ต๐‘–๐‘ ๐‘โ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘’ ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘ฅ๐‘ฆ๐‘™๐‘Ž๐‘ ๐‘’ ๐‘‚๐‘ฅ๐‘–๐‘‘๐‘Ž๐‘ ๐‘’
  • 26. ๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐ป โˆ’ ๐ถ โˆ’ ๐‘‚๐ป ๐‘‚ = ๐ถ โˆ’ ๐ป ๐ป2๐ถ โˆ’ ๐‘ถ๐‘ท๐‘ถ๐Ÿ‘ ๐Ÿโˆ’ ๐Ÿ ๐Ÿ ๐Ÿ‘ ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ) ๐Ÿ‘ โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’ โˆ’ ๐’ˆ๐’๐’š๐’„๐’†๐’“๐’‚๐’๐’…๐’†๐’‰๐’š๐’…๐’† (๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ) ๐Ÿ, ๐Ÿ‘ โˆ’ ๐‘ซ๐’Š๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’๐’ˆ๐’๐’š๐’„๐’†๐’“๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘จ๐‘ป๐‘ท ๐‘จ๐‘ซ๐‘ท ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ท๐’Š ๐Ÿ๐Ÿ ๐’Ž๐’๐’. ๐’†๐’‚๐’„๐’‰
  • 27. ๐‘‡โ„Ž๐‘’ 12 ๐‘ƒ๐บ๐ด๐ฟ ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘  ๐‘๐‘Ž๐‘› ๐‘๐‘’ ๐‘ข๐‘ก๐‘–๐‘™๐‘–๐‘ ๐‘’๐‘‘ ๐‘–๐‘› 4 ๐‘ค๐‘Ž๐‘ฆ๐‘ : 5 ร— [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 5 ร— [๐‘ซ๐‘ฏ๐‘จ๐‘ท] ๐‘‡๐‘Ÿ๐‘–๐‘œ๐‘ ๐‘’ ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘’ ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ โ‘ก โ‘ข [๐Ÿ“ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ๐Ÿ“ ๐‘ช] [๐Ÿ“ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ๐Ÿ“ ๐‘ช] [๐Ÿ“ ร— ๐‘ท] [๐Ÿ“ ร— ๐‘ท] 3 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 3 [๐‘ซ๐‘ฏ๐‘จ๐‘ท] [๐Ÿ‘ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ— ๐‘ช] [๐Ÿ‘ ร— ๐Ÿ‘ ๐‘ช = ๐Ÿ— ๐‘ช] + [๐Ÿ‘ ร— ๐‘ท] [๐Ÿ‘ ร— ๐‘ท] ๐ด๐‘™๐‘‘๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ, ๐Ÿ” โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”. [๐Ÿ‘ ร— ๐Ÿ” ๐‘ช = ๐Ÿ๐Ÿ– ๐‘ช] [๐Ÿ‘ ร— ๐Ÿ ๐‘ท] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ:
  • 28. 3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ, ๐Ÿ” โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”. 3 ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘Ž๐‘ ๐‘’ ๐Ÿ‘ ๐‘ท๐’Š โ‘  โ‘ก ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ’: ๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ฎ๐’๐’–๐’„๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ฎ๐‘ณ๐‘ผ๐‘ช๐‘ถ๐‘บ๐‘ฌ ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ ๐‘ท๐’Š [๐Ÿ” ๐‘ช] [๐Ÿ” ๐‘ช] [๐Ÿ” ๐‘ช]
  • 29. 2 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 2 [๐‘ญ๐’“๐’–๐’„๐’•๐’๐’”๐’† ๐Ÿ” โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’†] + [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] [๐Ÿ ร— ๐Ÿ” ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘˜๐‘’๐‘ก๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘ฌ๐’“๐’š๐’•๐’‰๐’“๐’๐’”๐’† ๐Ÿ’ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† + [๐Ÿ ร— ๐Ÿ“ ๐‘ช] [๐Ÿ ร— ๐Ÿ’ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ‘
  • 30. + [๐Ÿ ร— ๐Ÿ’ ๐‘ช] [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘Ž๐‘™๐‘‘๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ• โˆ’ ๐’…๐’Š๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘ฌ๐’“๐’š๐’•๐’‰๐’“๐’๐’”๐’† ๐Ÿ’ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ• ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ”: ๐‘บ๐’•๐’†๐’‘ ๐Ÿ 2 [๐‘ซ๐‘ฏ๐‘จ๐‘ท] [๐Ÿ ร— ๐‘ท] [๐Ÿ ร— ๐‘ท] [๐Ÿ ร— ๐Ÿ ๐‘ท] 2 ๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ• โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘Ž๐‘ก๐‘Ž๐‘ ๐‘’ [๐Ÿ ร— ๐Ÿ• ๐‘ช] [๐Ÿ ร— ๐‘ท] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ•: ๐Ÿ ๐‘ท๐’Š
  • 31. 2 [๐‘ท๐‘ฎ๐‘จ๐‘ณ] 2 [๐‘บ๐’†๐’…๐’๐’‰๐’†๐’‘๐’•๐’–๐’๐’๐’”๐’† ๐Ÿ• โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’†] + [๐Ÿ ร— ๐Ÿ‘ ๐‘ช] [๐Ÿ ร— ๐Ÿ• ๐‘ช] ๐‘‡๐‘Ÿ๐‘Ž๐‘›๐‘  โˆ’ ๐‘˜๐‘’๐‘ก๐‘œ๐‘™๐‘Ž๐‘ ๐‘’ 2 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 2 ๐‘น๐’Š๐’ƒ๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† + [๐Ÿ ร— ๐Ÿ“ ๐‘ช] [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ–:
  • 32. ๐‘บ๐’•๐’†๐’‘ ๐Ÿ—: 2 ๐‘ฟ๐’š๐’๐’–. ๐Ÿ“ โˆ’ ๐‘ท [๐Ÿ’ ร— ๐Ÿ“ ๐‘ช] 2 ๐‘ฟ๐’š๐’๐’–. ๐Ÿ“ โˆ’ ๐‘ท ๐‘บ๐’•๐’†๐’‘ ๐Ÿ“ ๐‘บ๐’•๐’†๐’‘ ๐Ÿ– 4 ๐‘ฟ๐’š๐’๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† 4 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† ๐ธ๐‘๐‘–๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ [๐Ÿ’ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ๐ŸŽ: 2 ๐‘น๐’Š๐’ƒ๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐ผ๐‘ ๐‘œ๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ ๐‘’ 2 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ ร— ๐Ÿ“ ๐‘ช] ๐‘บ๐’•๐’†๐’‘ ๐Ÿ–
  • 33. ๐‘บ๐’•๐’†๐’‘ ๐Ÿ๐Ÿ: 6 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ“ โˆ’ ๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ” ร— ๐Ÿ“ ๐‘ช] [๐Ÿ” ร— ๐‘ท] 6 ๐‘น๐’Š๐’ƒ๐’–๐’๐’๐’”๐’† ๐Ÿ, ๐Ÿ“ โˆ’ ๐’ƒ๐’Š๐’”๐’‘๐’‰๐’๐’”๐’‘๐’‰๐’‚๐’•๐’† [๐Ÿ” ร— ๐Ÿ“ ๐‘ช] [๐Ÿ” ร— ๐Ÿ ๐‘ท] ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘Ÿ๐‘–๐‘๐‘ข๐‘™๐‘œ๐‘ ๐‘’ ๐‘˜๐‘–๐‘›๐‘Ž๐‘ ๐‘’ ๐Ÿ” ๐‘จ๐‘ซ๐‘ท ๐Ÿ” ๐‘จ๐‘ป๐‘ท
  • 34. ๐Ÿ” ๐‘น๐’–๐‘ฉ๐‘ท + 6 ๐ถ๐‘‚2 + 6 ๐ป2๐‘‚ ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ + 12 ๐ด๐‘‡๐‘ƒ + 12 ๐‘๐ด๐ท๐‘ƒ๐ป + 12 ๐ป+ ๐Ÿ๐Ÿ [๐‘ท๐‘ฎ๐‘จ] ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ๐‘ณ + 12 ๐ด๐ท๐‘ƒ + 12 ๐‘ƒ๐‘– + 12 ๐‘๐ด๐ท๐‘ƒ+ ๐Ÿ๐Ÿ ๐‘ท๐‘ฎ๐‘จ๐‘ณ + 6 ๐ด๐‘‡๐‘ƒ ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ (๐‘ญ๐’“๐’–๐’„. ๐Ÿ” โˆ’ ๐‘ท) + ๐Ÿ” ๐‘น๐’–๐‘ฉ๐‘ท + 6 ๐ด๐ท๐‘ƒ + 6 ๐‘ƒ๐‘–
  • 35. ๐ถ๐‘œ๐‘š๐‘๐‘–๐‘›๐‘–๐‘›๐‘” ๐‘Ž๐‘™๐‘™ 3 ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘–๐‘œ๐‘›๐‘ : ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ + ๐Ÿ” ๐‘ฏ๐Ÿ๐‘ถ + 18 ๐ด๐‘‡๐‘ƒ + 12 [๐‘๐ด๐ท๐‘ƒ๐ป + ๐ป+] ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ + 18 [๐ด๐ท๐‘ƒ + ๐‘ƒ๐‘–] + 12 [๐‘๐ด๐ท๐‘ƒ+]
  • 36. ๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ๐‘ณ (๐Ÿ๐Ÿ) ๐Ÿ ๐Ÿ ๐Ÿ“ ๐Ÿ‘ ๐‘ซ๐‘ฏ๐‘จ๐‘ท ๐Ÿ ๐Ÿ‘ ๐‘ญ๐’“๐’–๐’„. ๐Ÿ, ๐Ÿ” โˆ’๐’…๐’Š๐’‘๐’‰๐’๐’”. ๐‘ญ๐’“๐’–๐’„. ๐Ÿ” โˆ’ ๐‘ท (๐Ÿ‘) (๐Ÿ‘) ๐‘ฏ๐‘ฌ๐‘ฟ๐‘ถ๐‘บ๐‘ฌ ๐Ÿ ๐Ÿ ๐‘ฟ๐’š๐’. ๐Ÿ“ โˆ’ ๐‘ท ๐‘ฌ๐’“๐’š. ๐Ÿ’ โˆ’ ๐‘ท (๐Ÿ) ๐‘บ๐’†๐’…. ๐Ÿ, ๐Ÿ• โˆ’ ๐’…๐’Š๐’‘. (๐Ÿ) ๐‘บ๐’†๐’…. ๐Ÿ• โˆ’ ๐‘ท (๐Ÿ) ๐‘น๐’Š๐’ƒ. ๐Ÿ“ โˆ’ ๐‘ท (๐Ÿ) (๐Ÿ’) ๐‘น๐’Š๐’ƒ๐’–. ๐Ÿ“ โˆ’ ๐‘ท (๐Ÿ”) ๐‘น๐’–๐‘ฉ๐‘ท ๐Ÿ‘ โˆ’ ๐‘ท๐‘ฎ๐‘จ (๐Ÿ”) ๐Ÿ, ๐Ÿ‘ โˆ’ ๐’…๐’Š๐‘ท๐‘ฎ๐‘จ (๐Ÿ๐Ÿ) (๐Ÿ๐Ÿ) โŸต ๐Ÿ” ๐‘ช๐‘ถ๐Ÿ โŸถ ๐Ÿ‘๐‘ท๐’Š โŸถ ๐Ÿ๐‘ท๐’Š โŸถ ๐Ÿ” ๐‘จ๐‘ซ๐‘ท โŸต ๐Ÿ” ๐‘จ๐‘ป๐‘ท ๐Ÿ๐Ÿ ๐‘จ๐‘ป๐‘ท ๐Ÿ๐Ÿ ๐‘จ๐‘ซ๐‘ท โ†“ โ†‘ ๐Ÿ๐Ÿ [๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+] ๐Ÿ๐Ÿ ๐‘ต๐‘จ๐‘ซ๐‘ท+ โ†“ โ†‘ ๐Ÿ๐Ÿ ๐‘ท๐’Š โ†˜
  • 37.
  • 38. ๐‘จ๐’๐’‚๐’•๐’๐’Ž๐’š ๐’๐’‡ ๐‘ช๐Ÿ’ ๐’๐’†๐’‚๐’—๐’†๐’” 2 ๐‘ก๐‘ฆ๐‘๐‘’๐‘  ๐‘œ๐‘“ ๐‘๐‘’๐‘™๐‘™๐‘ /๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  ๐‘ด๐’†๐’”๐’๐’‘๐’‰๐’š๐’๐’ ๐‘ช๐’†๐’๐’๐’” ๐‘ฉ๐’–๐’๐’…๐’๐’† ๐‘บ๐’‰๐’†๐’‚๐’•๐’‰ ๐‘ช๐’†๐’๐’๐’” โ€ข ๐‘†๐‘š๐‘Ž๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘  โ€ข ๐ฟ๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘›๐‘œ. ๐‘œ๐‘“ ๐‘›๐‘œ๐‘Ÿ๐‘š๐‘Ž๐‘™ ๐‘ ๐‘–๐‘ง๐‘’ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘Ž ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘…๐‘ข๐ต๐‘–๐‘ ๐ถ๐‘‚ ๐‘Ž๐‘๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘œ๐‘๐‘๐‘ข๐‘Ÿ๐‘  โ€ข ๐ฟ๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘๐‘’๐‘™๐‘™๐‘  โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐‘“๐‘’๐‘ค ๐‘™๐‘Ž๐‘Ÿ๐‘”๐‘’ ๐‘ ๐‘–๐‘ง๐‘’ ๐‘โ„Ž๐‘™๐‘œ๐‘Ÿ๐‘œ๐‘๐‘™๐‘Ž๐‘ ๐‘ก๐‘  โ€ข ๐บ๐‘Ÿ๐‘Ž๐‘›๐‘Ž ๐‘Ž๐‘๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘…๐‘ข๐ต๐‘–๐‘ ๐ถ๐‘‚ ๐‘๐‘Ÿ๐‘’๐‘ ๐‘’๐‘›๐‘ก โ€ข ๐‘‚๐‘›๐‘™๐‘ฆ ๐ท๐‘Ž๐‘Ÿ๐‘˜ ๐‘…๐‘’๐‘Ž๐‘๐‘› ๐‘œ๐‘๐‘๐‘ข๐‘Ÿ๐‘ 
  • 39. ๐ถ๐‘‚2 ๐’Š ๐‘ช๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’•๐’Š๐’๐’ โˆถ ๐ป2๐ถ๐‘‚3 ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘›๐‘–๐‘ ๐‘Ž๐‘›โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘Ž๐‘ ๐‘’ โˆ’๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ = ๐‘‚๐‘ƒ๐‘‚3 2โˆ’ ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ + ๐ป2๐‘‚ ๐‘ช๐’‚๐’“๐’ƒ๐’๐’ ๐’…๐’Š๐’๐’™๐’Š๐’…๐’† ๐‘ช๐’‚๐’“๐’ƒ๐’๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘ท๐‘ฌ๐‘ท ๐‘ช๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’”๐’† ๐‘ท๐’Š ๐‘ฏ๐Ÿ๐‘ช๐‘ถ๐Ÿ‘
  • 40. ๐’Š๐’Š ๐‘น๐’†๐’…๐’–๐’„๐’•๐’Š๐’๐’ โˆถ ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐ป๐‘‚ โˆ’ ๐ถ๐ป โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ด๐’‚๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐‘€๐‘Ž๐‘™๐‘–๐‘ ๐ท๐‘’โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘”๐‘’๐‘›๐‘Ž๐‘ ๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘‡โ„Ž๐‘’ ๐‘š๐‘Ž๐‘™๐‘–๐‘ ๐‘Ž๐‘๐‘–๐‘‘ ๐‘“๐‘œ๐‘Ÿ๐‘š๐‘’๐‘‘ โ„Ž๐‘’๐‘Ÿ๐‘’ ๐‘–๐‘  ๐‘ ๐‘’๐‘›๐‘ก ๐‘ก๐‘œ ๐‘กโ„Ž๐‘’ ๐‘๐‘ข๐‘›๐‘‘๐‘™๐‘’ ๐‘ โ„Ž๐‘’๐‘Ž๐‘กโ„Ž ๐‘๐‘’๐‘™๐‘™๐‘ .
  • 41. ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป3๐ถ โˆ’ ๐ป๐‘‚ โˆ’ ๐ถ๐ป โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป โˆ’ ๐‘ด๐’‚๐’๐’Š๐’„ ๐’‚๐’„๐’Š๐’… ๐’Š๐’Š๐’Š ๐‘ซ๐’†๐’„๐’‚๐’“๐’ƒ๐’๐’™๐’š๐’๐’‚๐’•๐’Š๐’๐’ โˆถ ๐‘€๐‘Ž๐‘™๐‘–๐‘ ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† + ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’†
  • 42. ๐’Š๐’— ๐‘น๐’†๐’ˆ๐’†๐’๐’†๐’“๐’‚๐’•๐’Š๐’๐’ ๐’๐’‡ ๐‘ท๐‘ฌ๐‘ท: ๐‘‚ = ๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป3๐ถ โˆ’ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘‡โ„Ž๐‘’ ๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘–๐‘  ๐‘ ๐‘’๐‘›๐‘ก ๐‘๐‘Ž๐‘๐‘˜ ๐‘ก๐‘œ ๐‘š๐‘’๐‘ ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘  ๐‘“๐‘œ๐‘Ÿ ๐‘๐‘œ๐‘›๐‘ฃ๐‘’๐‘Ÿ๐‘ ๐‘–๐‘œ๐‘› ๐‘–๐‘›๐‘ก๐‘œ ๐‘โ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘’๐‘›๐‘œ๐‘™ ๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’. โˆ’๐ถ โˆ’ ๐ถ๐‘‚๐‘‚๐ป ๐ป2๐ถ = ๐‘‚๐‘ƒ๐‘‚3 2โˆ’ ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ƒ๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘‘๐‘–๐‘˜๐‘–๐‘›๐‘Ž๐‘ ๐‘’ ๐‘จ๐‘ซ๐‘ท ๐‘จ๐‘ป๐‘ท ๐‘ƒโ„Ž๐‘œ๐‘ ๐‘โ„Ž๐‘œ๐‘’๐‘›๐‘œ๐‘™๐‘๐‘ฆ๐‘Ÿ๐‘ข๐‘ฃ๐‘Ž๐‘ก๐‘’ ๐‘๐‘Ž๐‘› ๐‘›๐‘œ๐‘ค ๐‘ก๐‘Ž๐‘˜๐‘’ ๐‘๐‘Ž๐‘Ÿ๐‘ก ๐‘–๐‘› ๐‘กโ„Ž๐‘’ ๐‘๐‘ฆ๐‘๐‘™๐‘’ ๐‘Ž๐‘”๐‘Ž๐‘–๐‘›.
  • 43. ๐‘ด๐’†๐’”๐’๐’‘๐’‰๐’š๐’๐’ ๐‘ช๐’†๐’๐’ ๐‘ฉ๐’–๐’๐’…๐’๐’† ๐‘บ๐’‰๐’†๐’‚๐’•๐’‰ ๐‘ช๐’†๐’๐’ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ท๐‘ฌ๐‘ท ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’‚๐’•๐’† ๐‘จ๐‘ซ๐‘ท โŸต ๐‘จ๐‘ป๐‘ท โŸถ โŸต ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ท๐’Š ๐‘ช๐‘ถ๐Ÿ + ๐‘ฏ๐Ÿ๐‘ถ ๐‘ฏ๐Ÿ๐‘ช๐‘ถ๐Ÿ‘ ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ด๐’‚๐’๐’‚๐’•๐’† โŸต ๐‘ต๐‘จ๐‘ซ๐‘ท+ โŸถ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ช๐‘ถ๐Ÿ ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’๐’‚๐’”๐’• ๐‘ช๐’‰๐’๐’๐’“๐’๐’‘๐’๐’‚๐’”๐’• ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’† ๐‘ฎ๐’๐’–๐’„๐’๐’”๐’†
  • 44.
  • 45. ๐ด๐‘ก ๐‘›๐‘–๐‘”โ„Ž๐‘ก, ๐‘กโ„Ž๐‘’ ๐‘ ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘Ž ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘œ๐‘๐‘’๐‘› ๐‘Ž๐‘™๐‘™๐‘œ๐‘ค๐‘–๐‘›๐‘” ๐ถ๐‘‚2 ๐‘ก๐‘œ ๐‘‘๐‘–๐‘“๐‘“๐‘ข๐‘ ๐‘’ ๐‘–๐‘›๐‘ก๐‘œ ๐‘กโ„Ž๐‘’ ๐‘š๐‘’๐‘ ๐‘œ๐‘โ„Ž๐‘ฆ๐‘™๐‘™ ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘ช๐‘ถ๐Ÿ ๐‘ฏ๐‘ช๐‘ถ๐Ÿ‘ โˆ’ + ๐‘ถ๐‘ฏ โˆ’ [๐‘ฉ๐’Š๐’„๐’‚๐’“๐’ƒ๐’๐’๐’‚๐’•๐’†] ๐‘ท๐‘ฌ๐‘ท ๐‘ท๐’‰๐’๐’”๐’‘๐’‰๐’๐’†๐’๐’๐’ ๐’‘๐’š๐’“๐’–๐’—๐’‚๐’•๐’† ๐‘ฏ๐‘ช๐‘ถ๐Ÿ‘ โˆ’ ๐‘ฏ๐Ÿ‘๐‘ท๐‘ถ๐Ÿ’ ๐‘ถ๐‘จ๐‘จ ๐‘ถ๐’™๐’‚๐’๐’๐’‚๐’„๐’†๐’•๐’‚๐’•๐’† ๐‘ถ๐‘จ๐‘จ ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘€๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐ท๐‘’โ„Ž๐‘ฆ๐‘‘๐‘Ÿ๐‘œ๐‘”๐‘’๐‘›๐‘Ž๐‘ ๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ƒ๐ธ๐‘ƒ ๐ถ๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘ฅ๐‘ฆ๐‘™๐‘Ž๐‘ ๐‘’
  • 46. ๐‘‡โ„Ž๐‘’ ๐‘š๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘’๐‘‘ ๐‘–๐‘  ๐‘ ๐‘ก๐‘œ๐‘Ÿ๐‘’๐‘‘ ๐‘–๐‘› ๐‘กโ„Ž๐‘’ ๐‘ฃ๐‘Ž๐‘๐‘ข๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘‡โ„Ž๐‘’ ๐‘Ž๐‘๐‘๐‘ข๐‘š๐‘ข๐‘™๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ ๐‘œ๐‘Ÿ๐‘”๐‘Ž๐‘›๐‘–๐‘ ๐‘Ž๐‘๐‘–๐‘‘๐‘  ๐‘๐‘Ž๐‘ข๐‘ ๐‘’๐‘  ๐‘กโ„Ž๐‘’ ๐‘Ž๐‘๐‘–๐‘‘๐‘–๐‘“๐‘–๐‘๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘œ๐‘“ ๐‘๐‘’๐‘™๐‘™๐‘ . ๐‘ด๐’‚๐’๐’‚๐’•๐’† ๐‘ท๐’š๐’“๐’–๐’—๐’‚๐’•๐’† + ๐‘ช๐‘ถ๐Ÿ ๐‘€๐‘Ž๐‘™๐‘Ž๐‘ก๐‘’ ๐‘’๐‘›๐‘ง๐‘ฆ๐‘š๐‘’ ๐‘ต๐‘จ๐‘ซ๐‘ท+ ๐‘ต๐‘จ๐‘ซ๐‘ท๐‘ฏ + ๐‘ฏ+ ๐‘ช๐’‚๐’๐’—๐’Š๐’ ๐‘ช๐’š๐’„๐’๐’† ๐ท๐‘ข๐‘Ÿ๐‘–๐‘›๐‘” ๐‘‘๐‘Ž๐‘ฆ๐‘ก๐‘–๐‘š๐‘’, ๐‘กโ„Ž๐‘’ ๐‘ ๐‘ก๐‘œ๐‘š๐‘Ž๐‘ก๐‘Ž ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘›๐‘ก ๐‘๐‘™๐‘œ๐‘ ๐‘’ & ๐‘๐‘Ÿ๐‘’๐‘ฃ๐‘’๐‘›๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘ ๐‘ ๐‘–๐‘ฃ๐‘’ ๐‘ค๐‘Ž๐‘ก๐‘’๐‘Ÿ ๐‘™๐‘œ๐‘ ๐‘ . ๐‘‡โ„Ž๐‘’ ๐ถ๐‘‚2 ๐‘™๐‘–๐‘๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘’๐‘‘ ๐‘’๐‘›๐‘ก๐‘’๐‘Ÿ๐‘  ๐ถ3 ๐ถ๐‘ฆ๐‘๐‘™๐‘’ ๐‘“๐‘œ๐‘Ÿ ๐‘๐‘Ž๐‘Ÿ๐‘๐‘œ๐‘› โˆ’ ๐‘“๐‘–๐‘ฅ๐‘Ž๐‘ก๐‘–๐‘œ๐‘› ๐‘ข๐‘ ๐‘–๐‘›๐‘” ๐‘กโ„Ž๐‘’ ๐‘’๐‘›๐‘’๐‘Ÿ๐‘”๐‘ฆ ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘ ๐‘“๐‘Ÿ๐‘œ๐‘š ๐ฟ๐‘–๐‘”โ„Ž๐‘ก ๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘–๐‘œ๐‘›.