求解 x^9*y^2=2yx

$$x ^ { 9 } \times y ^ { 2 } = 2 y x$$

求解 x 的值 (复数求解)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in 2^{\frac{5}{8}}\left(\frac{1}{2}+\frac{1}{2}i\right)y^{-\frac{1}{8}},\sqrt[8]{2}y^{-\frac{1}{8}},\sqrt[8]{2}iy^{-\frac{1}{8}},2^{\frac{5}{8}}\left(-\frac{1}{2}+\frac{1}{2}i\right)y^{-\frac{1}{8}},-\sqrt[8]{2}y^{-\frac{1}{8}},2^{\frac{5}{8}}\left(-\frac{1}{2}-\frac{1}{2}i\right)y^{-\frac{1}{8}},-\sqrt[8]{2}iy^{-\frac{1}{8}},2^{\frac{5}{8}}\left(\frac{1}{2}-\frac{1}{2}i\right)y^{-\frac{1}{8}}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

求解 y 的值 (复数求解)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{2}{x^{8}}\text{, }&x\neq 0\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

求解 x 的值

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt[8]{\frac{2}{y}}\text{; }x=-\sqrt[8]{\frac{2}{y}}\text{, }&y>0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

求解 y 的值

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{2}{x^{8}}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$