Question

The solution set of $\sqrt{2+x}>x$ is :

• A. (-1 , 2)
• B. $[-1,2]$
• C. $\{1,-2\}$
• D. None

Answer 1

The correct option is A (-1 , 2)

$\sqrt{2+x}>x$

$\Rightarrow 2+x>x^2$

$\Rightarrow x^2-x-2<0$

$\Rightarrow (x-2)(x+1)<0$

So $x\in (-1,2)$.