Solve x^2y^2=xy^2

$$x ^ { 2 } y ^ { 2 } = x y ^ { 2 }$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=1\text{ or }x=0\end{matrix}\right.$$

Steps by Finding Square Root

Subtract xy^{2} from both sides.

$$x^{2}y^{2}-xy^{2}=0$$

Combine all terms containing y.

$$\left(x^{2}-x\right)y^{2}=0$$

Dividing by x^{2}-x undoes the multiplication by x^{2}-x.

$$y^{2}=\frac{0}{x^{2}-x}$$

Divide 0 by x^{2}-x.

$$y^{2}=0$$

Take the square root of both sides of the equation.

$$y=0 y=0$$

The equation is now solved. Solutions are the same.

$$y=0$$

Steps Using the Quadratic Formula

Subtract xy^{2} from both sides.

$$x^{2}y^{2}-xy^{2}=0$$

Combine all terms containing y.

$$\left(x^{2}-x\right)y^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute x^{2}-x for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}}}{2\left(x^{2}-x\right)}$$

Take the square root of 0^{2}.

$$y=\frac{0±0}{2\left(x^{2}-x\right)}$$

Multiply 2 times x^{2}-x.

$$y=\frac{0}{2x\left(x-1\right)}$$

Divide 0 by 2x\left(-1+x\right).

$$y=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=1\text{ or }x=0\end{matrix}\right.$$