How to solve a twin root equation?

Question

I thought to factorize a sqrt(x), but I can't find out anything. I thought to multiply both sides with themselves four times, but I'm not sure that works.

Answer 1

HINT:

$x^{1/2}+x^{1/4}=x^{1/4}(x^{1/4}+1)$

now let

$y=x^{1/4}$

amd solve $y(y+1)=12$

Answer 2

You can take out an $x^\frac14$:

$$x^\frac14\left(x^\frac14+1\right)=12$$ And let $u=x^\frac14$, and thus you have:

$$u(u+1)=12$$

Obviously, $u=3$ (but you can also use quadratic formula to find this), so:

$$3=x^\frac14\\\therefore x=81$$