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AP EAMCET201921 Apr 2019Morning ShiftMathematicsQuadratic EquationActual

If satisfies the equation x 2 x+1 + 2 x+1 x =2 , then the roots of the equation ^2 x^2+4 x+3=0 are

Options

  1. A1,3
  2. B-1,1
  3. C2,-3
  4. D3,4

Correct answer

A. 1,3

Step-by-step solution

x 2 x+1 + 2 x+1 x =2 Let x 2 x+1 =y Then, y+ 1 y =2 aligned & y^2-2 y+1=0 & (y-1)(y-1)=0 & (y-1)^2=0 & y-1=0 & y=1 & y=1 & x 2 x+1 =1 & x 2 x+1 =1 & 2 x+1=x & x=-1 & aligned satisfies the Eq. (i), therefore =-1 Now, ^2 x^2+4 x+3=0 Put the value of aligned (-1)^2 x^2+4(-1) x+3 & =0 x^2-4 x+3 & =0 (x-1)(x-3) & =0 x & =1,3 aligned Hence, the roots of the equation ^2 x^2+4 x+3=0 are 1,3

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