Solve left(yxright)^2-4*x^2*1=0

$${ \left(yx \right) }^{ 2 } -4 \times { x }^{ 2 } \times 1=0$$

Solve for x (complex solution)

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

Steps by Finding Square Root

Expand \left(yx\right)^{2}.

$$y^{2}x^{2}-4x^{2}\times 1=0$$

Multiply 4 and 1 to get 4.

$$y^{2}x^{2}-4x^{2}=0$$

Combine all terms containing x.

$$\left(y^{2}-4\right)x^{2}=0$$

Dividing by y^{2}-4 undoes the multiplication by y^{2}-4.

$$x^{2}=\frac{0}{y^{2}-4}$$

Divide 0 by y^{2}-4.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Expand \left(yx\right)^{2}.

$$y^{2}x^{2}-4x^{2}\times 1=0$$

Multiply 4 and 1 to get 4.

$$y^{2}x^{2}-4x^{2}=0$$

Combine all terms containing x.

$$\left(y^{2}-4\right)x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2\left(y^{2}-4\right)}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2\left(y^{2}-4\right)}$$

Multiply 2 times y^{2}-4.

$$x=\frac{0}{2y^{2}-8}$$

Divide 0 by 2y^{2}-8.

$$x=0$$

Solve for y (complex solution)

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

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&|y|=2\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\in \mathrm{R}\text{, }&x=0\\y=2\text{; }y=-2\text{, }&x\neq 0\end{matrix}\right.$$