Resolver x^3-y^3=0009+3(x-y)

$$x ^ { 3 } - y ^ { 3 } = 0009 + 3 ( x - y )$$

Resolva para x (complex solution)

$$x=\frac{\sqrt{12-3y^{2}}-y}{2}$$

$$x=\frac{-\sqrt{12-3y^{2}}-y}{2}$$

$$x=y$$

Resolva para y (complex solution)

$$y=\frac{\sqrt{12-3x^{2}}-x}{2}$$

$$y=\frac{-\sqrt{12-3x^{2}}-x}{2}$$

$$y=x$$

Resolva para x

$$\left\{\begin{matrix}\\x=y\text{, }&\text{unconditionally}\\x=\frac{\sqrt{12-3y^{2}}-y}{2}\text{; }x=\frac{-\sqrt{12-3y^{2}}-y}{2}\text{, }&|y|\leq 2\end{matrix}\right,$$

Resolva para y

$$\left\{\begin{matrix}\\y=x\text{, }&\text{unconditionally}\\y=\frac{\sqrt{12-3x^{2}}-x}{2}\text{; }y=\frac{-\sqrt{12-3x^{2}}-x}{2}\text{, }&|x|\leq 2\end{matrix}\right,$$