\(\left\{{}\begin{matrix}y=x^2\\\frac{1}{x}=\frac{1}{y}+\frac{1}{z}\\z=xy\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x^2\\\frac{1}{x}=\frac{1}{y}+\frac{1}{xy}\\z=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=x^2\\\frac{1}{x}=\frac{x}{xy}+\frac{1}{xy}=\frac{x+1}{xy}\\z=xy\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x^2\\xy=x^2+x\\z=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=x^2\\x^3-x^2-x=0\\z=xy\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x^2\\x\left(x^2-x-1\right)=0\\z=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=0\left(loại\right)\\\left(x-\frac{1}{2}\right)^2=\frac{5}{4}\end{matrix}\right.\\y=x^2\\z=xy\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=\frac{\sqrt{5}+1}{2}\left(TM\right)\\x=\frac{1-\sqrt{5}}{2}\left(TM\right)\end{matrix}\right.\\y=x^2\\z=xy\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\frac{1+\sqrt{5}}{2}\left(\right)TM\\y=\frac{3+\sqrt{5}}{2}\left(TM\right)\\z=2+\sqrt{5}\left(TM\right)\end{matrix}\right.\\\left\{{}\begin{matrix}x=\frac{1-\sqrt{5}}{2}\\y=\frac{3-\sqrt{5}}{2}\left(TM\right)\\z=2-\sqrt{5}\left(TM\right)\end{matrix}\right.\end{matrix}\right.\)
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