Question

\(\left\{{}\begin{matrix}\left(\sqrt{x}+1\right)\left(\sqrt{y}-1\right)=\sqrt{xy}\\\left(\sqrt{x}-1\right)\left(\sqrt{y}+3\right)=\sqrt{xy}\end{matrix}\right.\)

Answer 1

ĐKXĐ: \(x\ge0;y\ge0\)

\(\left\{{}\begin{matrix}\sqrt{xy}-\sqrt{x}+\sqrt{y}-1=\sqrt{xy}\\\sqrt{xy}+3\sqrt{x}-\sqrt{y}-3=\sqrt{xy}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}-\sqrt{x}+\sqrt{y}=1\\3\sqrt{x}-\sqrt{y}=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2\sqrt{x}=4\\3\sqrt{x}-\sqrt{y}=3\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\sqrt{x}=2\\\sqrt{y}=3\sqrt{x}-3=3\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=4\\y=9\end{matrix}\right.\)