Tìm x, y sao cho $5x-2\sqrt{x}\left(2+y\right)+y^2+1=0$.

minhthu_

$5x-2\sqrt{x}\left(2+y\right)+y^2+1=0$

$5x-4\sqrt{x}-2y\sqrt{x}+y^2+1=0$

$\left(y^2-2y\sqrt{x}+x)+\left(\left(2\sqrt{x}\right)^2-4\sqrt{x}+1\right)=0\right.$

$\left(y-\sqrt{x}\right)^2+\left(2\sqrt{x}-1\right)^2=0$

$\left\lbrace_{\left(2\sqrt{x}-1\right)^2=0}^{\left(y-\sqrt{x}\right)^2=0}\right.$

$\left\lbrace_{2\sqrt{x}-1=0}^{y-\sqrt{x}=0}\right.$

$\left\lbrace_{y=\frac{1}{2}}^{x=\frac{1}{4}}\right.$