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AP EAMCET201921 Apr 2019Morning ShiftMathematicsFunctionsActual

The set of all real numbers satisfying the inequation x^2-|x+2|+x>0 is

Options

  1. A[-2,- 2 ) ( 2 , )
  2. B(- ,-2) (2, )
  3. C(- ,- 2 ) ( 2 , )
  4. D(- ,-2) ( 2 , )

Correct answer

C. (- ,- 2 ) ( 2 , )

Step-by-step solution

x^2-|x+2|+x>0 Case I If x+2 0 aligned & x^2-(x+2)+x>0 |x|= array cc x, & x 0 -x, & x 0 & (x- 2 )(x+ 2 )=0 & + -2- 2 2 & x [-2,- 2 ] [ 2 , ] & aligned Case II x+2 0 & x^2+2 x+2>0 & (x+1)^2+1>0 x < -2 aligned Hence, the solution set is x (- ,- 2 ) ( 2 , )

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