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The set of all real numbers x for which ...

The set of all real numbers x for which `x^2-|x+2| +x gt 0` is

A

`(-oo,-2uu(2oo)`

B

`(-oo,-sqrt2)uu(sqrt2,oo)`

C

`(-oo,-1)uu(1,oo)`

D

`(sqrt2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `x^(2)-|x+2|+x gt0" "...(i)`
Case I When `x+2 ge 0`
`thereforex^(2)-x-2+gt0impliesx^(2)-2gt0`
`impliesxlt-sqrt2or x gtsqrt2`
`implies x in[-2,-sqrt2)uu(sqrt2,oo)" "(ii)`
Case II When `x+2lt0`
`thereforex^(2)+x+2+xgt0`
`impliesx^(2)+2x+2 gt0`
`implies(x+1)^(2)+1gt0`
which is true for all x,
`thereforexle -2orin(-oo,-2)" "...(iii)`
From Eqs. (ii) and (iii), we get
`x in(-oo,-sqrt2)uu(sqrt2,oo)`
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