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