Solve fy=x^3-2

$$f y = x ^ { 3 } - 2$$

Solve for f (complex solution)

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

Steps for Solving Linear Equation

The equation is in standard form.

$$yf=x^{3}-2$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Solve for f

$$\left\{\begin{matrix}f=\frac{x^{3}-2}{y}\text{, }&y\neq 0\\f\in \mathrm{R}\text{, }&x=\sqrt[3]{2}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yf=x^{3}-2$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Solve for x (complex solution)

$$x=e^{\frac{2\pi i}{3}}\sqrt[3]{fy+2}$$

$$x=\sqrt[3]{fy+2}$$

$$x=e^{\frac{4\pi i}{3}}\sqrt[3]{fy+2}$$

Solve for x

$$x=\sqrt[3]{fy+2}$$