ĐKXĐ: ...
\(\sqrt{\left(x+y\right)\left(x-y\right)}-\sqrt{x+y}+1-\sqrt{x-y}=0\)
\(\Leftrightarrow\sqrt{x+y}\left(\sqrt{x-y}-1\right)-\left(\sqrt{x-y}-1\right)=0\)
\(\Leftrightarrow\left(\sqrt{x+y}-1\right)\left(\sqrt{x-y}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+y=1\\x-y=1\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y}=1\\x+y=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x+y+2\sqrt{xy}=1\\x+y=1\end{matrix}\right.\)
\(\Leftrightarrow xy=0\Rightarrow\left(x;y\right)=\left(1;0\right);\left(0;1\right)\)
Th2: \(\left\{{}\begin{matrix}y=x-1\\\sqrt{x}+\sqrt{y}=1\end{matrix}\right.\) \(\Leftrightarrow\sqrt{x}+\sqrt{x-1}=1\)
\(\Leftrightarrow\frac{x-1}{\sqrt{x}+1}+\sqrt{x-1}=0\Leftrightarrow x=1\Rightarrow y=0\)
