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AP EAMCET20227 Jul 2022Evening ShiftMathematicsBasics of MathematicsActual

x^4 (x^2+1 ) (x^2+3 ) =

Options

  1. AA x+B x^2+1 + C x+D x^2+3 for some A, B, C, D R 0
  2. BA x+B x^2+1 + C x x^2+1 for some A, B, C R 0
  3. CA x x^2+1 + B x x^2+3 for some A, B R 0
  4. D1+ A x+B x^2+1 + C x+D x^2+3 for some A, B, C, D R

Correct answer

D. 1+ A x+B x^2+1 + C x+D x^2+3 for some A, B, C, D R

Step-by-step solution

aligned x^4 (x^2+1 ) (x^2+3 ) & = (x^2+1 ) (x^2+3 )-3 x^2-x^2-3 (x^2+1 ) (x^2+3 ) & =1- 4 x^2+3 (x^2+1 ) (x^2+3 ) & =1+ A x+B x^2+1 + C x+D x^2+3 aligned

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