Question

Let $x=\sqrt{4+\sqrt{4-x}}$. Then x equals:

• A. 3
• B.
• C.
• D.

Answer 1

The correct option is C

$x=\sqrt{4+\sqrt{4-x}}$
$⟹x^2=4+\sqrt{4-x}⟹(x^2-4)=\sqrt{4-x}$
Only option (c) satisfies this condition.

Shortcut : Reverse Gear
$x=\sqrt{4}$ + small value (note the minus signs in between)
$\Rightarrow$ the answer is something slightly greater than 2.
Look for an answer option, which is slightly greater than 2.
(a) 3 is much greater than 2.
(b) $\frac{(\sqrt{13}-1)}{2}\approx 1.1$ (this can never be the answer)
(c) $\frac{(\sqrt{13}+1)}{2}\approx 2.2$ (this is a possible answer)
(d) $\sqrt{13}=$ something greater than 3. This is also not possible, as the value is too high.