解決z=x-y/x^3-y^3 |Microsoft數學求解器

$$z = \frac { x - y } { x ^ { 3 } - y ^ { 3 } }$$

解 x

$$\left\{\begin{matrix}x=\frac{-\sqrt{-3y^{2}+\frac{4}{z}}-y}{2}\text{, }&z\leq \frac{4}{3y^{2}}\text{ and }z>0\text{ and }\left(y>0\text{ or }z\neq \frac{1}{3y^{2}}\right)\text{ and }y\neq 0\\x=\frac{\sqrt{-3y^{2}+\frac{4}{z}}-y}{2}\text{, }&z\leq \frac{4}{3y^{2}}\text{ and }z>0\text{ and }\left(y<0\text{ or }z\neq \frac{1}{3y^{2}}\right)\text{ and }y\neq 0\end{matrix}\right.$$

解 y

$$\left\{\begin{matrix}y=\frac{-\sqrt{-3x^{2}+\frac{4}{z}}-x}{2}\text{, }&z\leq \frac{4}{3x^{2}}\text{ and }z>0\text{ and }\left(x>0\text{ or }z\neq \frac{1}{3x^{2}}\right)\text{ and }x\neq 0\\y=\frac{\sqrt{-3x^{2}+\frac{4}{z}}-x}{2}\text{, }&z\leq \frac{4}{3x^{2}}\text{ and }z>0\text{ and }\left(x<0\text{ or }z\neq \frac{1}{3x^{2}}\right)\text{ and }x\neq 0\end{matrix}\right.$$