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AP EAMCET202017 Sep 2020Morning ShiftMathematicsQuadratic EquationActual

If (x R ), then one of the solutions of ( x+1 -| x-1 |= 4 x-1 ) among the following is

Options

  1. A(x= 5 4 )
  2. B(x= -5 4 )
  3. C(x=0 )
  4. D(x=1 )

Correct answer

A. (x= 5 4 )

Step-by-step solution

( aligned & x+1 -| x-1 |= 4 x-1 & x+1 - 4 x-1 =| x-1 | aligned ) Squaring on both sides ( array ll & x+1+4 x-1-2 (x+1)(4 x-1) =x-1 & 5 x-2 (x+1)(4 x-1) =x-1 & 4 x+1=2 (x+1)(4 x-1) array ) Squaring on both sides ( array lll & 16 x^2+1+8 x=4 (4 x^2+3 x-1 ) & 16 x^2+8 x+1=16 x^2+12 x-4 & 4 x=5 x= 5 4 array )

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