Solve x^3sqrt{a-x^2}=0

$$x ^ { 3 } \sqrt { a - x ^ { 2 } } = 0$$

Solve for a

$$\left\{\begin{matrix}\\a=x^{2}\text{, }&\text{unconditionally}\\a\geq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Divide both sides by x^{3}.

$$\frac{x^{3}\sqrt{a-x^{2}}}{x^{3}}=\frac{0}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$\sqrt{a-x^{2}}=\frac{0}{x^{3}}$$

Divide 0 by x^{3}.

$$\sqrt{a-x^{2}}=0$$

Square both sides of the equation.

$$a-x^{2}=0$$

Subtract -x^{2} from both sides of the equation.

$$a-x^{2}-\left(-x^{2}\right)=-\left(-x^{2}\right)$$

Subtracting -x^{2} from itself leaves 0.

$$a=-\left(-x^{2}\right)$$

Subtract -x^{2} from 0.

$$a=x^{2}$$

Solve for a (complex solution)

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

Solve for x (complex solution)

$$x=\sqrt{a}$$

$$x=0$$

$$x=-\sqrt{a}$$

Solve for x

$$x=-\sqrt{a}$$

$$x=0$$

$$x=\sqrt{a}\text{, }a\geq 0$$