ĐKXĐ: \(x\ne\left\{0;1\right\}\)
Đặt \(\sqrt[5]{\frac{16x}{x-1}}=t\)
\(\Rightarrow t+\frac{1}{t}=\frac{5}{2}\Leftrightarrow2t^2-5t+2=0\Rightarrow\left[{}\begin{matrix}t=2\\t=\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt[5]{\frac{16}{x-1}}=2\\\sqrt[5]{\frac{16}{x-1}}=\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\frac{16x}{x-1}=32\\\frac{16x}{x-1}=\frac{1}{32}\end{matrix}\right.\)
\(\Rightarrow x=...\)