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ĐKXĐ: $y\geq 0$
$2A=\left ( x-\sqrt{y} \right )^{2}+\left ( -1-x \right )^{2}+\left ( \sqrt{y}-1 \right )^{2}\geq \frac{\left ( x-\sqrt{y}-1-x+\sqrt{y}-1 \right )^{2}}{3}$
Vậy $Amin=\frac{2}{3}\Leftrightarrow x-\sqrt{y}=-1-x=\sqrt{y}-1\Leftrightarrow x=\frac{-1}{3}, y=\frac{1}{9}$
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