AP EAMCET202421 May 2024Morning ShiftMathematicsBasics of MathematicsActual
If 1 (3 x+1)(x-2) = A 3 x+1 + B x-2 and x+1 (3 x+1)(x-2) = C 3 x+1 + D x-2 , then
Options
- AA+3 B=0, A: C=1: 3, B: D=2: 3
- BA+3 B=0, A: C=3: 1, B: D=3: 2
- CA-3 B=0, A: C=3: 2, B: D=1: 3
- DA+3 B=0, A: C=3: 2, B: D=1: 3
Correct answer
D. A+3 B=0, A: C=3: 2, B: D=1: 3
Step-by-step solution
aligned & 1 (3 x+1)(x-2) = A 3 x+1 + B x-2 & 1 (3 x+1)(x-2) = 3 3 x+1 - 1 x-2 ( -1 7 ) & = - 3 7 3 x+1 + 4 7 x-2 ~A = -3 7 , ~B = 1 7 & x+1 (3 x+1)(x-2) = x-2+3 (3 x+1)(x-2) & = 1 3 x+1 - 3 7 [ 3 3 x+1 - 1 x-2 ] & = 1 3 x+1 - 9 7(3 x+1) + 3 7 (x-2) = -2 7 3 x+1 + 3 7 x-2 & ~A = -3 7 , ~B = 1 7 , C = -2 7 , D = 3 7 & ~A +3 ~B =0, ~A : C =3: 2, ~B : D =1: 3 aligned