(2) $\Leftrightarrow (y-1)^{2}=(x^{2}+y^{2})(1-x^{2}-y^{2})$$\Rightarrow x^{2}+y^{2}\leq 1 \Rightarrow |x| \leq 1$
mà $(x^{2}+y^{2})(1-x^{2}-y^{2})\leq \frac{1}{4}$
$\Rightarrow (y-1)^{2}\leq \frac{1}{4}$
$\Leftrightarrow \frac{1}{2}\leq y\leq \frac{3}{2} \Rightarrow y>0, |x|\leq 1$
$(\sqrt{x^{2}+1}+1) (x^{2}-y^{3}+3y-2)=(\sqrt{x^{2}+1}+1)(x^{2}-(y-1)^{2}(y+2))$
$\leq (\sqrt{x^{2}+1}+1)x^{2} \leq (\sqrt{2}+1)x^{2}\leq 4x^{2}$
$\Rightarrow x=0;y=1$