\(\left\{{}\begin{matrix}\sqrt{x}+\sqrt{y+1}=1\\\sqrt{y}+\sqrt{x+1}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+1+2\sqrt{x\left(y+1\right)}=1\\y+x+1+2\sqrt{y\left(x+1\right)}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+2\sqrt{x\left(y+1\right)}=0\\x+y+2\sqrt{y\left(x+1\right)}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+2\sqrt{x\left(y+1\right)}=0\\x+y+2\sqrt{y\left(x+1\right)}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2\sqrt{x\left(y+1\right)}=-x-y\\2\sqrt{y\left(x+1\right)}=-x-y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x\left(y+1\right)}=\dfrac{-x-y}{2}\\\sqrt{y\left(x+1\right)}=\dfrac{-x-y}{2}\end{matrix}\right.\)
\(\Rightarrow\sqrt{x\left(y+1\right)}=\sqrt{y\left(x+1\right)}\\ \Leftrightarrow xy+x=xy+y\\ \Leftrightarrow x=y\)
Rồi đến đây bạn tự làm nhé
