AP EAMCET202421 May 2024Morning ShiftMathematicsLimitsActual
If _ x ( 2 x+1 + 2 x-1 )^8+( 2 x+1 - 2 x-1 )^8 (P x^4-16 ) (x+ x^2-2 )^8+ (x- x^2-2 )^8 =1 , then P=
Options
- A16
- B64
- C1 64
- D1 16
Correct answer
D. 1 16
Step-by-step solution
_ x [( 2 x+1 + 2 x-1 )^8+( 2 x+1 - 2 x-1 )^8 ] (P x^4-16 ) (x+ x^2-2 )^8+ (x- x^2-2 )^8 Dividing numerator and denominator by x^8 aligned & _ x [ ( 2+ 1 x + 2- 1 x )^8+ ( 2+ 1 x - 2- 1 x )^8 ] (P- 16 x^4 ) (1+ 1- 2 x^2 )^8+ (1- 1- 2 x^2 )^8 & =1 aligned Apply the limit aligned & [( 2+0 + 2-0 )^8+( 2 - 2 )^8 ] P (1+1)^8+(1-1)^8 =1 & 2^4 P =1 P = 1 16 aligned