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AP EAMCET2009MathematicsBinomial Theorem

If x is numerically so small so that x^2 and higher powers of x can be neglected, then (1+ 2 x 3 )^ 3 / 2 (32+5 x)^ -1 / 5 is approximately equal to

Options

  1. A32+31 x 64
  2. B31+32 x 64
  3. C31-32 x 64
  4. D1-2 x 64

Correct answer

A. 32+31 x 64

Step-by-step solution

aligned (1+ & . 2 x 3 )^ 3 / 2 (32+5 x)^ -1 / 5 & = [1+ 3 2 ( 2 x 3 ) ](32)^ -1 / 5 (1+ 5 32 x )^ -1 / 5 aligned (Neglect higher powers of x ) =[1+x] 2⁻¹ [1- 1 5 ( 5 32 ) x ] (Neglect higher powers of x ) aligned & = 1 2 (1+x) (1- x 32 ) & = (1+x)(32-x) 64 = 32+31 x 64 aligned (Neglect x^2 term)

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