Resol x^4+y^4=1

$$x ^ { 4 } + y ^ { 4 } = 1$$

Resoleu x (complex solution)

$$x=i\sqrt[4]{1-y^{4}}$$

$$x=\sqrt[4]{1-y^{4}}$$

$$x=-\sqrt[4]{1-y^{4}}$$

$$x=-i\sqrt[4]{1-y^{4}}$$

Resoleu y (complex solution)

$$y=i\sqrt[4]{1-x^{4}}$$

$$y=\sqrt[4]{1-x^{4}}$$

$$y=-\sqrt[4]{1-x^{4}}$$

$$y=-i\sqrt[4]{1-x^{4}}$$

Resoleu x

$$\left\{\begin{matrix}x=\sqrt{-\sqrt{1-y^{2}}}\sqrt[4]{y^{2}+1}\text{; }x=-\sqrt{-\sqrt{1-y^{2}}}\sqrt[4]{y^{2}+1}\text{, }&|y|=1\\x=\sqrt[4]{1-y^{4}}\text{; }x=-\sqrt[4]{1-y^{4}}\text{, }&|y|\leq 1\end{matrix}\right,$$

Resoleu y

$$\left\{\begin{matrix}y=\sqrt{-\sqrt{1-x^{2}}}\sqrt[4]{x^{2}+1}\text{; }y=-\sqrt{-\sqrt{1-x^{2}}}\sqrt[4]{x^{2}+1}\text{, }&|x|=1\\y=\sqrt[4]{1-x^{4}}\text{; }y=-\sqrt[4]{1-x^{4}}\text{, }&|x|\leq 1\end{matrix}\right,$$