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AP EAMCET201922 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

If (x ) is so small, that (x^5 ) and higher power of (x ) may be neglected, then the coefficient of (x^4 ) in the expansion of ( x^2+4 - x^2+9 ), is

Options

  1. A( 19 1728 )
  2. B( -19 1728 )
  3. C( 43 1728 )
  4. D( -43 1728 )

Correct answer

B. ( -19 1728 )

Step-by-step solution

Given, ( x^2+4 - x^2+9 ) ( aligned & = (x^2+4 )^ 1 2 - (x^2+9 )^ 1 2 & =2 (1+ x^2 4 )^ 1 2 -3 (1+ x^2 9 )^ 1 2 aligned ) Now, coefficient of (x^4 ) is ( [2 1 2 ( 1 2 -1 ) 2 ! ( x^2 4 )^2-3 ( 1 2 ( 1 2 -1 ) 2 ! ( x^2 9 )^2 ] ] ) ( aligned & =x^4 [- 1 4 16 +3 1 8 1 81 ]=x^4 [- 1 64 + 1 216 ] & Coefficient of x^4 is (- 1 64 + 1 216 ) & = -216+64 (64)(216) = -152 (64)(216) = -19 1728 aligned )

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