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AP EAMCET20228 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

If x (x-1) (x^2+1 )^2 = 1 4 [ 1 x-1 - x+1 x^2+1 ]+y , then y =

Options

  1. A1 2 [ 1-x (x^2+1 )^2 ]
  2. B1+x 3 (x^2+1 )^2
  3. C1-x (x^2-1 )^2
  4. D1+x (x^2+1 )^2

Correct answer

A. 1 2 [ 1-x (x^2+1 )^2 ]

Step-by-step solution

Let f(x)= cases 1 2 (-x-) & if x 1 cases x = A ( x ^2+1 )^2+( Bx + c )( x -1) ( x ^2+1 )+( Dx + E )( x -1) On putting n =1,0,-1,2,-2 and after solving we get aligned & A = 1 4 ; B = -1 4 ; C = -1 4 ; & D = -1 2 and E = 1 2 aligned x ( x -1) ( x ^2+1 )^2 = 1 4 [ 1 x -1 - x +1 x ^2+1 ]+ 1 2 1- x ( x ^2+1 )^2 ] y = 1 2 [ 1- x ( x ^2+1 )^2 ]

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