ĐKXĐ : \(\left\{{}\begin{matrix}x\ge2\\y\ge-\dfrac{1}{2}\end{matrix}\right.\)
Ta có \(\left\{{}\begin{matrix}x+2y-1-2\sqrt{2xy+x-4y-2}=0\\\sqrt{x-2}+3\sqrt{2y+1}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-2\right)+\left(2y+1\right)-2\sqrt{\left(x-2\right)\left(2y+1\right)}=0\\\sqrt{x-2}+3\sqrt{2y+1}=4\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x-2}-\sqrt{2y+1}\right)^2=0\\\sqrt{x-2}+3\sqrt{2y+1}=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=\sqrt{2y+1}\\4\sqrt{2y+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=\sqrt{2y+1}\\2y+1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=\sqrt{2y+1}\\y=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-2}=1\\y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=0\end{matrix}\right.\)
