The set of all real numbers satisfying the inequation x^2- |x+2 |+x0 is

Question

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

Accepted Answer

Correct answer: C. (c) Given x^2- |x+2 |+x>0 Case I: When x+2 0 x^2- (x+2 )+x>0 ⇒x^2-2>0 ⇒ (x- 2 ) (x+ 2 )=0 outside of the roots x ∈ [-2 ,- 2 ] ∪ [ 2 , ] Case II: When x+2<0 x^2+ (x+2 )+x>0 ⇒x^2+2x+2>0 ⇒ (x+1 )^2+1>0 ⇒x<-2 Hence, the solution set is x ∈ (- ,- 2 ) ∪ ( 2 , )

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

Solution

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