\(\left\{{}\begin{matrix}3\sqrt{x-1}-\frac{1}{3}\sqrt{y+1}=5\\5\sqrt{x-1}-2\sqrt{y+1}=4\end{matrix}\right.\) (đk: \(x\ge1;y\ge-1\))
\(\Leftrightarrow\left\{{}\begin{matrix}18\sqrt{x-1}-2\sqrt{y+1}=30\\5\sqrt{x-1}-2\sqrt{y+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}13\sqrt{x-1}=26\\5\sqrt{x-1}-2\sqrt{y+1}=4\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}=2\\2\sqrt{y+1}=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=4\\y+1=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\left(tm\right)\\y=8\left(tm\right)\end{matrix}\right.\)
vậy hệ phương trình có nghiệm (x;y)=(5;8)
