sqrt[3]{18x^4y^3/12z^3}=y を解きます| Microsoft 数学ソルバー

$$\sqrt[ 3 ] { \frac { 18 x ^ { 4 } y ^ { 3 } } { 12 z ^ { 3 } } } = y$$

x を解く (複素数の解)

$$\left\{\begin{matrix}x=\frac{\sqrt[4]{2}i\times \left(3z\right)^{\frac{3}{4}}}{3}\text{; }x=\frac{\sqrt[4]{2}\times \left(3z\right)^{\frac{3}{4}}}{3}\text{; }x=-\frac{\sqrt[4]{2}\times \left(3z\right)^{\frac{3}{4}}}{3}\text{; }x=-\frac{\sqrt[4]{2}i\times \left(3z\right)^{\frac{3}{4}}}{3}\text{, }&z\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\frac{2\pi }{3}\right)\\x\in \mathrm{C}\text{, }&y=0\text{ and }z\neq 0\end{matrix}\right.$$

y を解く (複素数の解)

$$\left\{\begin{matrix}y\in \mathrm{C}\text{, }&\left(x=-\frac{\sqrt[4]{2}i\times \left(3z\right)^{\frac{3}{4}}}{3}\text{ or }x=-\frac{\sqrt[4]{2}\times \left(3z\right)^{\frac{3}{4}}}{3}\text{ or }x=\frac{\sqrt[4]{2}i\times \left(3z\right)^{\frac{3}{4}}}{3}\text{ or }x=\frac{\sqrt[4]{2}\times \left(3z\right)^{\frac{3}{4}}}{3}\right)\text{ and }|\frac{arg(y^{3})}{3}-arg(y)|<\frac{2\pi }{3}\text{ and }y\neq 0\text{ and }z\neq 0\\y=0\text{, }&z\neq 0\end{matrix}\right.$$

x を解く

$$\left\{\begin{matrix}x=\frac{\sqrt[4]{54}z^{\frac{3}{4}}}{3}\text{; }x=-\frac{\sqrt[4]{54}z^{\frac{3}{4}}}{3}\text{, }&z>0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z\neq 0\end{matrix}\right.$$

y を解く

$$\left\{\begin{matrix}y=0\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&z=\frac{\frac{2^{\frac{2}{3}}}{2}\times \left(3x\right)^{\frac{4}{3}}}{3}\text{ and }x\neq 0\end{matrix}\right.$$