ta có: \(\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)=1\)
Đặt : \(\sqrt{\left(5-2\sqrt{6}\right)^x}=a\) ; \(a\ge0\)
=> \(a+\frac{1}{a}=10\)
\(\Leftrightarrow a^2+1=10a\)
\(\Leftrightarrow a^2-10a+1=0\)
\(\Leftrightarrow a^2-2.5a+25-24=0\)
\(\Leftrightarrow\left(a-5\right)^2=24\)
\(\Leftrightarrow\orbr{\begin{cases}a-5=2\sqrt{6}\\a-5=-2\sqrt{6}\end{cases}\Rightarrow\orbr{\begin{cases}a=2\sqrt{6}+5\\a=5-2\sqrt{6}\end{cases}}}\)(TMĐK)
với \(a=5+2\sqrt{6}\)
=> \(\sqrt{\left(5-2\sqrt{6}\right)^x}=5+2\sqrt{6}\)
\(\Rightarrow\frac{1}{\left(5+2\sqrt{6}\right)^x}=\left(5+2\sqrt{6}\right)^2\)
=> x= -2
với \(a=5-2\sqrt{6}\)
=> \(\sqrt{\left(5-2\sqrt{6}\right)^x}=5-2\sqrt{6}\) =>x=2
vậy x=2 hoặc x=-2
