Giải phương trình: 1) $$\color{green}{\begin{cases}x^3+\sqrt{x^2+1}+\sqrt{x^2-y^2}=y^3+\sqrt{y^2+1} \\ x^3+2y+3-2\sqrt{y^3-1}= (x^2+2x+3)\sqrt{xy-y+1} \end{cases}}$$
2) $$\color{green}{\begin{cases}\sqrt[3]{x^3-3\sqrt{x+1}-5}+x^2y=x-1+(y-1)^3 \\ (x-y)[(x+y+1)^2+1]=2y(x^2-xy+x-y) \end{cases}}$$
3) $\begin{cases} \sqrt{2x^2-6xy+5y^2}+\sqrt{2x^2+2xy+13y^2}=2(x+y)\\ (x+2y)\sqrt{x+2}-4y^2\sqrt y=8y^4 \sqrt y-2\sqrt{x+2} \end{cases}$
4) $\frac{x}{\sqrt{33x^2-32x+8}}+\frac{2(2x-1)}{\sqrt{20x^2-12x+1}}=1$.
5)
$$\color{green}{\begin{cases}(1-y)\sqrt{x^2+2y^2}=x+2y+3xy \\ \sqrt{y+1}+\sqrt{x^2+2y^2}=2y-x \end{cases}}$$