`~rai~`
`2x-2\sqrt{x}-2\sqrt{xy}+y+1=0(ĐKXĐ:x;y≥0)`
`⇔x+x-2\sqrt{x}-2\sqrt{xy}+y+1=0`
`⇔(x-2\sqrt{x}+1)+(x-2\sqrt{xy}+1)=0`
`⇔(\sqrt{x}-1)^2+(\sqrt{x}-\sqrt{y})^2=0`
`text{Ta có:}`
`(\sqrt{x}-1)^2 ≥ 0 ∀x ∈R;(\sqrt{x}-\sqrt{y})^2 ≥0 ∀x;y∈R`
`⇔(\sqrt{x}-1)^2+(\sqrt{x}-sqrt{y})^2 ≥ 0 ∀x;y∈R`
`mà (\sqrt{x}-1)^2+(\sqrt{x}-\sqrt{y})^2=0`
`⇒` $\left \{ {({\sqrt{x}-1)^{2}=0} \atop {(\sqrt{x}-\sqrt{y})^{2}=0}} \right.$
`⇔` $\left \{ {{\sqrt{x}-1=0} \atop {\sqrt{x}-\sqrt{y}=0}} \right.$
`⇔` $\left \{ {{\sqrt{x}=1} \atop {\sqrt{x}-\sqrt{y}=0}} \right.$
`⇔` $\left \{ {{x=1} \atop {\sqrt{x}-\sqrt{y}=0}} \right.$
`⇔` $\left \{ {{x=1} \atop {1-\sqrt{y}=0}} \right.$
`⇔` $\left \{ {{x=1} \atop {\sqrt{y}=1}} \right.$
`⇔` $\left \{ {{x=1} \atop {y=1}} \right.$ .
`text{Vậy x=1;y=1.}`
