ĐKXĐ: ...
\(\Leftrightarrow\left\{{}\begin{matrix}x+\frac{1}{x}+y+\frac{1}{y}=\frac{9}{2}\\\left(x+\frac{1}{x}\right)\left(y+\frac{1}{y}\right)=5\end{matrix}\right.\)
Theo Viet đảo, \(x+\frac{1}{x}\) và \(y+\frac{1}{y}\) là nghiệm:
\(t^2-\frac{9}{2}t+5=0\Rightarrow\left[{}\begin{matrix}t=2\\t=\frac{5}{2}\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}x+\frac{1}{x}=2\\y+\frac{1}{y}=\frac{5}{2}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x^2-2x+1=0\\2y^2-5y+2=0\end{matrix}\right.\)
Th2: \(\left\{{}\begin{matrix}2x^2-5x+2=0\\y^2-2y+1=0\end{matrix}\right.\)
