ĐK:$x,y\epsilon R$
hpt$\Leftrightarrow \begin{cases}\sqrt{4-(x^{2}y-1)^{2}}=2x^{6}-x^{4}+y^{4}(1)\\ 1+\sqrt{1+(x-y)^{2}}=x^{3}(x^{3}-x+2y^{2})(2) \end{cases}$Lấy$ (1)-(2),$ta đc:$\sqrt{4-(x^{2}y-1)^{2}}-1-\sqrt{1+(x-y)^{2}}=(x^{3}-y^{2})^{2}\geq0$
$\Leftrightarrow \sqrt{4-(x^{2}y-1)^{2}}\geq1+\sqrt{1+(x-y)^{2}}\Leftrightarrow \begin{cases}x=y \\ x^{2}y=1 \end{cases}$
$\Leftrightarrow \begin{cases}x=1 \\ y=1 \end{cases}$