Question

Let $x=\sqrt{4+\sqrt{4-x}}$ Then x equals : (CAT 2005)

• A. 3
• B.
• C.
• D.

Answer 1

The correct option is C

Ans :(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
$X=\sqrt{4}+a$ small value ( note the minus signs inbetween )
$\Rightarrow$ 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) $\frac{(\sqrt{13}-1)\sim }{2}1.1$ (this can never be the answer)
(c) $\frac{(\sqrt{13}+1)\sim }{2}2.2$ (this is a possible answer)
(d) $\sqrt{13}=$ something greater than 3. this is also not possible, as the value is too high