Résoudre sqrt{x^2}-y^4+z^3=284

$$\sqrt { x ^ { 2 } } - y ^ { 4 } + z ^ { 3 } = 284$$

Calculer x (solution complexe)

$$\left\{\begin{matrix}x=y^{4}-z^{3}+284\text{; }x=-y^{4}+z^{3}-284\text{, }&arg(y^{4}-z^{3}+284)<\pi \\x=0\text{, }&y=-i\sqrt[4]{z^{3}-284}\text{ or }y=-\sqrt[4]{z^{3}-284}\text{ or }y=i\sqrt[4]{z^{3}-284}\text{ or }y=\sqrt[4]{z^{3}-284}\end{matrix}\right,$$

Calculer y (solution complexe)

$$y=i\sqrt[4]{z^{3}+\sqrt{x^{2}}-284}$$

$$y=\sqrt[4]{z^{3}+\sqrt{x^{2}}-284}$$

$$y=-\sqrt[4]{z^{3}+\sqrt{x^{2}}-284}$$

$$y=-i\sqrt[4]{z^{3}+\sqrt{x^{2}}-284}$$

Calculer x

$$x=y^{4}-z^{3}+284$$

$$x=-y^{4}+z^{3}-284\text{, }y^{4}-z^{3}+284\geq 0$$

Calculer y

$$y=\sqrt[4]{z^{3}+|x|-284}$$

$$y=-\sqrt[4]{z^{3}+|x|-284}\text{, }z=\sqrt[3]{-|x|+284}\text{ or }|x|\geq 284-z^{3}$$