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