Løs xyz*xy*x=2002

$$xyz \times xy \times x=2002$$

Løs for x (complex solution)

$$x=\sqrt[3]{2002}e^{\frac{2\pi i}{3}}y^{-\frac{2}{3}}z^{-\frac{1}{3}}$$

$$x=\sqrt[3]{2002}y^{-\frac{2}{3}}z^{-\frac{1}{3}}$$

$$x=\sqrt[3]{2002}e^{\frac{4\pi i}{3}}y^{-\frac{2}{3}}z^{-\frac{1}{3}}\text{, }y\neq 0\text{ and }z\neq 0$$

Løs for y (complex solution)

$$y=-\sqrt{2002}x^{-\frac{3}{2}}z^{-\frac{1}{2}}$$

$$y=\sqrt{2002}x^{-\frac{3}{2}}z^{-\frac{1}{2}}\text{, }x\neq 0\text{ and }z\neq 0$$

Løs for x

$$x=\frac{\sqrt[3]{\frac{2002}{z}}}{y^{\frac{2}{3}}}$$

$$y\neq 0\text{ and }z\neq 0$$

Løs for y

$$y=\sqrt{\frac{2002}{zx^{3}}}$$

$$y=-\sqrt{\frac{2002}{zx^{3}}}\text{, }\left(x>0\text{ and }z>0\right)\text{ or }\left(z<0\text{ and }x<0\right)$$