Question
If x is real and satisfies x + 2 > √x+4, then
Answer: Option B
:
B
Given, x + 2 > √x+4 ⇒ (x+2)2>(x+4) but inequality sign will be remained same if both sides are positive or negative.
R.H.S is positive and so L.H.S will also be positive.
Thus x>-2
⇒x2+4x+4>x+4 ⇒x2+3x>0
⇒ x(x+3)>0⇒ x<−3orx>0 ⇒ x>0
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:
B
Given, x + 2 > √x+4 ⇒ (x+2)2>(x+4) but inequality sign will be remained same if both sides are positive or negative.
R.H.S is positive and so L.H.S will also be positive.
Thus x>-2
⇒x2+4x+4>x+4 ⇒x2+3x>0
⇒ x(x+3)>0⇒ x<−3orx>0 ⇒ x>0
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