CAT 2024

Slot 2

QA

Question & Solution

Squaring on both sides, we get:

$x+6\sqrt{\ 2}+x-6\sqrt{\ 2}-2\left(x^2-72\right)^{\frac{1}{2}}=8$
$x-\left(x^2-72\right)^{\frac{1}{2}}=4$

Bringing x to the other side, we get:
$-\left(x^2-72\right)^{\frac{1}{2}}=4-x$
Squaring on both sides again, we get:

$x^2-72=16+x^2-8x$
$8x=88$
$x=11$

Therefore, 11 is the correct answer.