DK; $x\geq y\geq 0$pt(1) $\Leftrightarrow (1-y)(\sqrt{x-y}-1)+x-y-1-(x-y-1)\sqrt{y}=0$ $\Leftrightarrow (x-y-1)(\frac{1-y}{\sqrt{x-y}+1}+1-\sqrt{y})=0$ $\Leftrightarrow (x-y-1)(1-\sqrt{y})(\frac{1+\sqrt{y}}{\sqrt{x-y}+1}+1)=0$ $\Leftrightarrow x-y-1=0$ of y=1 do $(...)>04+) $y=1 \Rightarrow x=3 \Rightarrow (x;y)=(3;1)$+) $x=y+1 $ (2) $\Leftrightarrow 2y^{2}+3y-2=\sqrt{1-y}$ $\Leftrightarrow 2(y^{2}+y-1)+y-\sqrt{1-y}=04 $\Leftrightarrow (y^{2}+y-1)(2+\frac{1}{y+\sqrt{1-y}})=0$ $\Leftrightarrow y^{2}+y-1=0$ do (... )>0 $\Leftrightarrow y=\frac{-1+\sqrt{5}}{2}(tm )$ of $y=\frac{-1-\sqrt{5}}{2} (L)$ $\Leftrightarrow (x;y)=(\frac{1+\sqrt{5}}{2};\frac{-1+\sqrt{5}}{2})$

DK; $x\geq y\geq 0$pt(1) $\Leftrightarrow (1-y)(\sqrt{x-y}-1)+x-y-1-(x-y-1)\sqrt{y}=0$ $\Leftrightarrow (x-y-1)(\frac{1-y}{\sqrt{x-y}+1}+1-\sqrt{y})=0$ $\Leftrightarrow (x-y-1)(1-\sqrt{y})(\frac{1+\sqrt{y}}{\sqrt{x-y}+1}+1)=0$ $\Leftrightarrow x-y-1=0$ of y=1 do $(...)>04+) $y=1 \Rightarrow x=3 \Rightarrow (x;y)=(3;1)$+) $x=y+1 $ (2) $\Leftrightarrow 2y^{2}+3y-2=\sqrt{1-y}$ $\Leftrightarrow 2(y^{2}+y-1)+y-\sqrt{1-y}=0$ $\Leftrightarrow (y^{2}+y-1)(2+\frac{1}{y+\sqrt{1-y}})=0$ $\Leftrightarrow y^{2}+y-1=0$ do (... )>0 $\Leftrightarrow y=\frac{-1+\sqrt{5}}{2}(tm )$ of $y=\frac{-1-\sqrt{5}}{2} (L)$ $\Leftrightarrow (x;y)=(\frac{1+\sqrt{5}}{2};\frac{-1+\sqrt{5}}{2})$