0\\
a^x=5+2\sqrt{6}\\
\sqrt{5+2\sqrt{6}}^x=5+2\sqrt{6}\\
x=2
" alt=" \sqrt{5+\sqrt{24}}^x+(\sqrt{5-\sqrt{24}})^x=10\\
5-\sqrt{24}=\frac{1}{5+\sqrt{24}}=\frac{1}{a}\\
a^x+\frac{1}{a^x}=10\\
a^{2x}-10a^x+1=0\\
a^x=t\\
t^2-10t+1=0\\
D=100-4*1*1=\sqrt{96}=4\sqrt{6}\\
t=\frac{10+4\sqrt{6}}{2}=5+2\sqrt{6}>0\\
a^x=5+2\sqrt{6}\\
\sqrt{5+2\sqrt{6}}^x=5+2\sqrt{6}\\
x=2
" align="absmiddle" class="latex-formula">