ĐK: \(x\ne0\)
Đặt \(x-\frac{1}{x}=t\) \(\Rightarrow t^2=x^2+\frac{1}{x^2}-2\)
\(PT\Leftrightarrow2\left(t^2+2\right)-7t+2=0\)
\(\Leftrightarrow2t^2-7t+6=0\) \(\Leftrightarrow\left(t-2\right)\left(2t-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}t=2\\t=\frac{3}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{x}=2\\x-\frac{1}{x}=\frac{3}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-2x-1=0\\2x^2-3x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\pm\sqrt{2}\\x=2\\x=-\frac{1}{2}\end{matrix}\right.\) (tm)