Question

\(x-y+1=2\sqrt{x-y}-\sqrt{x-2}\)

Answer 1

\(x\ge2;x\ge y\)

\(\Leftrightarrow x-y-2\sqrt{x-y}+1=-\sqrt{x-2}\)

\(\Leftrightarrow\left(\sqrt{x-y}-1\right)^2=-\sqrt{x-2}\) (1)

Mà \(\left\{{}\begin{matrix}\left(\sqrt{x-y}-1\right)^2\ge0\\-\sqrt{x-2}\le0\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-y}-1=0\\\sqrt{x-2}=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)