\(\left\{{}\begin{matrix}4\sqrt{x+3}-9\sqrt{y+1}=2\\5\sqrt{x+3}+3\sqrt{y+1}=31\end{matrix}\right.\left(I\right)\)
Đặt \(:\left\{{}\begin{matrix}t=\sqrt{x+3}\\u=\sqrt{y+1}\end{matrix}\right.\)
\(\left(I\right):\left\{{}\begin{matrix}4t-9u=2\\5t+3u=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4t-9u=2\\15t+9u=93\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}19t=95\\15t+9u=93\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}t=5\\15.5+9u=93\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}t=5\\u=2\end{matrix}\right.\)
Với \(:\left\{{}\begin{matrix}t=5\\u=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\sqrt{x+3}=5\\\sqrt{y+1}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x+3=25\\y+1=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=22\\y=3\end{matrix}\right.\)
Vậy nghiệm hệ phương trình là (22; 3)
