Đk $x;y\ge0$$\sqrt{x+1}+\sqrt{y}=\sqrt{y+1}+\sqrt{x}$$\Leftrightarrow x+1+y+2\sqrt{y(x+1)}=y+1+x+2\sqrt{x(y+1)}$$\Leftrightarrow \sqrt{xy+y}=\sqrt{xy+x}\Leftrightarrow xy+y=xy+x\Leftrightarrow x=y$
Đk $x;y\ge0$$\sqrt{x+1}+\sqrt{y}=\sqrt{y+1}+\sqrt{x}$$\Leftrightarrow x+1+y+2\sqrt{y(x+1)}=y+1+x+2\sqrt{x(y+1)}$$\Leftrightarrow \sqrt{xy+y}=\sqrt{xy+x}\Leftrightarrow x=y$
Đk $x;y\ge0$$\sqrt{x+1}+\sqrt{y}=\sqrt{y+1}+\sqrt{x}$$\Leftrightarrow x+1+y+2\sqrt{y(x+1)}=y+1+x+2\sqrt{x(y+1)}$$\Leftrightarrow \sqrt{xy+y}=\sqrt{xy+x}\Leftrightarrow x
y+y=xy+x\Leftrightarrow x=y$