cat 2024 Question 18

Question

If $(x + 6\sqrt{2})^{\cfrac{1}{2}} - (x - 6\sqrt{2})^{\cfrac{1}{2}} = 2\sqrt{2}$, then x equals

Accepted Answer

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.

Question 18.