<s>[INST] 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
 [/INST] Expanding on @DanielFischer's comment, let $y=(\sqrt{3}+\sqrt{2})^x$ so $y+1/y=10$ and $y=5\pm2\sqrt{6}$, so $x=\pm2$.
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