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AP EAMCET202418 May 2024Morning ShiftMathematicsBinomial TheoremActual

The absolute value of the difference of the coefficients of x^4 and x^6 in the expansion of 2 x^2 (x^2+1 ) (x^2+2 ) is

Options

  1. A13 4
  2. B1 4
  3. C9 4
  4. D1

Correct answer

A. 13 4

Step-by-step solution

Since 2 x^2 (x^2+1 ) (x^2+2 ) = -2 x^2+1 + 4 x^2+2 =-2 (1+x^2 )⁻¹+ 4 2 (1+ x^2 2 )⁻¹=-2 (1+x^2 )⁻¹+2 (1+ x^2 2 )⁻¹=-2 (1-x^2+x^4-x^6+ . )+2 (1- x^2 2 + x^4 4 - x^6 8 + . ) So, co-efficient of x^4=-2+ 1 2 = -3 2 and co-efficient of x^6=2- 1 4 = 7 4 Now, required value = 7 4 + 3 2 = 13 4

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