DEVOIR B - Semestre 1 - 3APIC Dr. Karam Ouharou .pdf

1. .
1
Exercice
𝑃 = (
√2−√3
√2
:
1
√2+√3
) ×
√2
4√3
𝑃 = −
√3
12
𝑄 = −2√48 + 3√192 − 4√75
𝑄 𝑎√𝑏(𝑎 ∈ ℤ; 𝑏 ∈ ℕ)
𝑄
𝑃 𝑄
𝑃(𝑃 − 1) =
𝑃−1
𝑄
.
2
Exercice
𝐴 = (√5 − √3)2
𝐵 = 𝑥2
− 7𝑥 + 10
𝐴
𝐶 =
1
2
(√5 − √8 − 2√15)
𝐵 𝒙 = √2
.
3
Exercice
𝑥 𝑦 𝑎√𝑏 𝑎 𝑏
𝑥 = 2√50 − 3√18 + √200 − √2
𝑦 = √20 + √80 −
√32
√12
× √48
𝑚 = 1 − 2√3 𝑛 = 1 + √12
𝑚2
𝑛2
𝑚 + 𝑛, 𝑚 × 𝑛
𝑚2
+ 𝑛2
𝑝 =
𝑚
𝑛
𝑝
.
4
Exercice

2. 𝐺 =
√
76 − 2
√
37 −
√
21
25
+
1
25
× √6 + √103 − 2√
9
4
𝐴𝐵𝐶 𝐴 𝐴𝐶 = √3 − 1 𝐵𝐶 = 2√2
𝐴𝐵2
𝐴𝐵 = √3 + 1 𝐴𝐵𝐶
1
𝐴𝐶
.
5
Exercice
b (𝑎 ≠ 0 𝑏 ≠ 0) ; 𝐹 =
(𝑎2𝑏−2)
−5
((𝑎3)2𝑏−4)−2
𝐹 = (𝑎𝑏)2
𝑎 = 5 × 10−5
𝑏 = 1015
𝐹
𝐹
𝐴 𝐴 =
𝑎𝑛𝑏−𝑎𝑛+1
𝑏𝑛𝑎−𝑏𝑛+1
× (
𝑎
𝑏
)
−𝑛
𝑛
𝑎 ≠ 𝑏; 𝑎 ≠ 1; 𝑎 ≠ −1
.
6
Exercice
1
√1+√2
+
1
√2+√3
+
1
√3+√4
+ ⋯ +
1
√99+√100
= 9 ; (1 +
1
𝑛
−
1
𝑛+1
)
2
= 1 +
1
𝑛2 +
1
(𝑛+1)2 (𝑛