Solve fx^4-a^4=0

$$f x ^ { 4 } - a ^ { 4 } = 0$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\left(\frac{a}{x}\right)^{4}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&a=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a^{4} to both sides. Anything plus zero gives itself.

$$fx^{4}=a^{4}$$

The equation is in standard form.

$$x^{4}f=a^{4}$$

Divide both sides by x^{4}.

$$\frac{x^{4}f}{x^{4}}=\frac{a^{4}}{x^{4}}$$

Dividing by x^{4} undoes the multiplication by x^{4}.

$$f=\frac{a^{4}}{x^{4}}$$

Solve for f

$$\left\{\begin{matrix}f=\left(\frac{a}{x}\right)^{4}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&a=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add a^{4} to both sides. Anything plus zero gives itself.

$$fx^{4}=a^{4}$$

The equation is in standard form.

$$x^{4}f=a^{4}$$

Divide both sides by x^{4}.

$$\frac{x^{4}f}{x^{4}}=\frac{a^{4}}{x^{4}}$$

Dividing by x^{4} undoes the multiplication by x^{4}.

$$f=\frac{a^{4}}{x^{4}}$$

Solve for a (complex solution)

$$a=i\sqrt[4]{f}x$$

$$a=\sqrt[4]{f}x$$

$$a=-\sqrt[4]{f}x$$

$$a=-i\sqrt[4]{f}x$$

Solve for a

$$\left\{\begin{matrix}a=0\text{, }&x=0\text{ or }f=0\\a=\sqrt[4]{f}x\text{; }a=-\sqrt[4]{f}x\text{, }&f\geq 0\end{matrix}\right.$$