AP EAMCET20224 Jul 2022Evening ShiftMathematicsBasics of MathematicsActual
If 13 x + 43 2 x 2 + 17 x + 30 = A 2 x + 5 + B x + 6 , then A 2 + B 2 =
Options
- A22 3
- B52
- C34
- D18 5
Correct answer
C. 34
Step-by-step solution
Given: 13 x + 43 2 x 2 + 17 x + 30 = A 2 x + 5 + B x + 6 ⇒ 13 x + 43 2 x 2 + 17 x + 30 = A x + 6 + B 2 x + 5 2 x + 5 x + 6 ⇒ 13 x + 43 2 x 2 + 17 x + 30 = A + 2 B x + 6 A + 5 B 2 x 2 + 17 x + 30 ⇒ A + 2 B x + 6 A + 5 B = 13 x + 43 On comparing, we get A + 2 B = 13       . . . . i 6 A + 5 B = 43       . . . . ii On solving i   &   ii , we get 7 B = 35 ⇒ B = 5 A = 13 - 2 B = 3 So, A 2 + B 2 = 9 + 25 = 34