If x is real and satisfies x-2-x-4- then

The correct option is D Given, x + 2 gt; √(x+4) nbsp; ⇒ (x+2)^2 gt; (x+4) but inequality sign will be remained same if both sides are positive or nega ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

If x is real ...

Question

If x is real and satisfies x + 2 > $\sqrt{x + 4}$ , then

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Solution

The correct option is B

Given, x + 2 > $\sqrt{x + 4}$ ⇒ $(x + 2)^{2} > (x + 4)$ 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

⇒ $x^{2} + 4 x + 4 > x + 4$ ⇒ $x^{2} + 3 x > 0$

⇒ $x (x + 3) > 0$ ⇒ $x < - 3 o r x > 0$ ⇒ $x > 0$

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If x is real and satisfies x + 2 > √x+4, then

The correct option is 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<−3 or x>0 ⇒ x>0

If x is real and satisfies x + 2 > $\sqrt{x + 4}$ , then