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Question

The set of all real x for which x2|x+2|+x0 is:

A
(,2)(2,)
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B
(,2][2,)
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C
(,1)(1,)
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D
(2,)
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Solution

The correct option is B (,2][2,)
x<2x2+x+2+x0
or x2+2x+20
or (x+1)2+10 which is true for all x
x<2
x2x2x2+x0
or x220
or x2 or x2
x ϵ (,2][2,+)
Solution is:
x ϵ(,2)(,2][2,)
i.e.,(,2][2,+)

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