Решете xdivy+ydivx=-1x^3

$$x \div y+y \div x=-1 { x }^{ 3 }$$

Решаване за x (complex solution)

$$x=-\frac{iy^{-\frac{1}{2}}\sqrt{2\left(\sqrt{1-4y^{3}}+1\right)}}{2}$$

$$x=\frac{iy^{-\frac{1}{2}}\sqrt{2\left(\sqrt{1-4y^{3}}+1\right)}}{2}$$

$$x=\frac{y^{-\frac{1}{2}}\sqrt{2\left(\sqrt{1-4y^{3}}-1\right)}}{2}$$

$$x=-\frac{y^{-\frac{1}{2}}\sqrt{2\left(\sqrt{1-4y^{3}}-1\right)}}{2}\text{, }y\neq 0$$

Решаване за y (complex solution)

$$y=\frac{x\left(\sqrt{x^{6}-4}-x^{3}\right)}{2}$$

$$y=-\frac{2x}{-\sqrt{x^{6}-4}+x^{3}}\text{, }x\neq 0$$

Решаване за x

$$x=\frac{\sqrt{-\frac{2\left(\sqrt{1-4y^{3}}+1\right)}{y}}}{2}$$

$$x=-\frac{\sqrt{-\frac{2\left(\sqrt{1-4y^{3}}+1\right)}{y}}}{2}\text{, }y<0$$

Решаване за y

$$y=-\frac{2x}{-\sqrt{x^{6}-4}+x^{3}}$$

$$y=\frac{x\left(\sqrt{x^{6}-4}-x^{3}\right)}{2}\text{, }|x|\geq \sqrt[3]{2}$$