\(xy+yz+xz=2xyz\Rightarrow\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2\Rightarrow\frac{1}{z^2}=\left(2-\frac{1}{x}-\frac{1}{y}\right)^2\)
Thay \(\frac{1}{z^2}=\left(2-\frac{1}{x}-\frac{1}{y}\right)^2\)vào pt \(\frac{2}{xy}=4+\frac{1}{z^2}\) ta đc pt:
\(\frac{2}{xy}=4+4+\frac{1}{x^2}+\frac{1}{y^2}-\frac{4}{x}-\frac{4}{y}+\frac{2}{xy}\)
\(\Leftrightarrow\left(\frac{1}{x^2}-\frac{4}{x}+4\right)+\left(\frac{1}{y^2}-\frac{4}{y}+4\right)=0\)
\(\Leftrightarrow\left(\frac{1}{x}-2\right)^2+\left(\frac{1}{y}-2\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\frac{1}{x}=2\\\frac{1}{y}=2\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{1}{2}\end{cases}}\Rightarrow z=-\frac{1}{2}}\)
Vậy nghiệm của hpt là (x;y;z)=(1/2;1/2;-1/2)
