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Chapter 7 solution of equations
1. Chapter 7 Solution of Equations
Algebraic Equations
Solve the following equations:
7 3 5
1. a) x 5 7x 4 x3 x2 7x 1 0 Ans. 1,
2
3 13 1 5
b) x 4 4x 3 x2 4x 1 0 Ans. ,
2 2
c) ( x 1)(x 2)(x 3)(x 4) 24 Ans. 0, 5
1 1
d) 36x 4 13x 2 1 0 Ans. ,
2 3
x2 y2 9
2. a)
y x 2 Ans. (2,1), (1,2)
3
1
x y
3 x 2 5 xy 2 y 2 0 9 217 3(9 217)
b) Ans. (2, 4), ( , )
x 2 2 y 2 6x 4 y 8 0 17 17
4
x 1
y 4 1
c) Ans. ( ,20), ( ,5)
4 5 5
y 25
x
x y 2 xy
1 1
d) y z 3 yz Ans. (0,0,0), ( , 1, )
3 4
z x 7 zx
4 x 3 3x 2 y y 3 8 1 3 1 3 1 3 1
e) Ans. (1,1), (3 ,3 ) , ( ,4 )
2 x 3 2 x 2 y xy 2 1 5 5 10 10
3x 2 5 y 2 7
f) Ans. (2,1), ( 2, 1), (3,2), ( 3, 2)
3xy 4 y 2 2
xy x y 1 6
g) yz y z 1 12 Ans. (1,2,3), ( 3, 4, 5)
zx z x 1 8
2. Trigonometric Equations
Find the general solutions (express in radian) of following equations
2n
1. 2 cos( 3 x ) 1 0 Ans. n
6 3 12 18
3x 4n 2
2. 2 sin 1 0 Ans. ( 1) n 1
n
4 3 9
x
3. tan( ) 3 Ans. 4n n
4 3
4. sin x 1 cos x Ans. n ( 1) n n
4 4
5. 3 sin x cos x 3 Ans. n ( 1) n n
3 6
6. ( 3 1) cos x ( 3 1) sin x 2 Ans. 2n n
4 12