Solve sqrt{x}-sqrt{y}=2

$$\sqrt{ x } - \sqrt{ y } =2$$

Solve for x

$$x=\left(\sqrt{y}+2\right)^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Subtract -\sqrt{y} from both sides of the equation.

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

Subtracting -\sqrt{y} from itself leaves 0.

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

Subtract -\sqrt{y} from 2.

$$\sqrt{x}=\sqrt{y}+2$$

Square both sides of the equation.

$$x=\left(\sqrt{y}+2\right)^{2}$$

Solve for y

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

$$x\geq 0\text{ and }\sqrt{x}-2\geq 0$$

Steps for Solving Radical Equations

Subtract \sqrt{x} from both sides of the equation.

$$-\sqrt{y}+\sqrt{x}-\sqrt{x}=2-\sqrt{x}$$

Subtracting \sqrt{x} from itself leaves 0.

$$-\sqrt{y}=2-\sqrt{x}$$

Subtract \sqrt{x} from 2.

$$-\sqrt{y}=-\sqrt{x}+2$$

Divide both sides by -1.

$$\frac{-\sqrt{y}}{-1}=\frac{-\sqrt{x}+2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{y}=\frac{-\sqrt{x}+2}{-1}$$

Divide 2-\sqrt{x} by -1.

$$\sqrt{y}=\sqrt{x}-2$$

Square both sides of the equation.

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

Solve for x (complex solution)

$$x=\left(\sqrt{y}+2\right)^{2}$$

$$arg(\sqrt{y}+2)<\pi$$

Solve for y (complex solution)

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

$$x=4\text{ or }arg(\sqrt{x}-2)<\pi$$