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If x is real and satisfies x +2lt sqrt(x...

If `x` is real and satisfies `x +2lt sqrt(x +4)`, then

A

`x lt - 2`

B

`x gt 0`

C

`-3lt x lt 0`

D

`-3 lt x lt 4`

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The correct Answer is:
B
If `x` is real and satisfies ………..
Given `x+2 gt sqrt(X +4) implies (x +2)^(2)gt (x+4)`
`implies x^(2)+4x+4gt x +4 implies x^(2)+3x gt 0`
`implies x(x+3)gt 0 implies x lt - 3 or x gt 0`
`implies x gt 0 (x+2` must be positive).
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