Square-root equation 
Solve square-root equation: $\left (\sqrt{5+2\sqrt{6}}  \right )^x+\left (\sqrt{5-2\sqrt{6}}  \right )^x=10$

$\left (\sqrt{5+2\sqrt{6}}  \right )^x+\left (\sqrt{5-2\sqrt{6}}  \right )^x=10\\
\left (\sqrt{\left (\sqrt{3}+\sqrt{2}  \right )^2} \right )^x+\left (\sqrt{\left (\sqrt{3}-\sqrt{2}  \right )^2} \right )^x=10\\
\left (\sqrt{3}+\sqrt{2} \right )^x+\left (\sqrt{3}-\sqrt{2} \right )^x=10$
at the moment I don't know what to do

As an alternative, 
quadratic with roots $\alpha=\sqrt{3}+ 2$ and $\beta=\sqrt{3}-2$ is  $x^2-2\sqrt{3}x+1=0$
Sum of roots is  $\alpha+\beta=2\sqrt{3}$
$\alpha^2+\beta^2=(\alpha+\beta)^2 - 2\alpha\beta = 12-2(1) = 10$
