Solve sqrt{x-3}+sqrt{3-x}=0

$$\sqrt { x - 3 } + \sqrt { 3 - x } = 0$$

Solve for x

$$x=3$$

Solution Steps

Subtract \sqrt{3-x} from both sides of the equation.

$$\sqrt{x-3}=-\sqrt{3-x}$$

Square both sides of the equation.

$$\left(\sqrt{x-3}\right)^{2}=\left(-\sqrt{3-x}\right)^{2}$$

Calculate \sqrt{x-3} to the power of 2 and get x-3.

$$x-3=\left(-\sqrt{3-x}\right)^{2}$$

Expand \left(-\sqrt{3-x}\right)^{2}.

$$x-3=\left(-1\right)^{2}\left(\sqrt{3-x}\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$x-3=1\left(\sqrt{3-x}\right)^{2}$$

Calculate \sqrt{3-x} to the power of 2 and get 3-x.

$$x-3=1\left(3-x\right)$$

Use the distributive property to multiply 1 by 3-x.

$$x-3=3-x$$

Add x to both sides.

$$x-3+x=3$$

Combine x and x to get 2x.

$$2x-3=3$$

Add 3 to both sides.

$$2x=3+3$$

Add 3 and 3 to get 6.

$$2x=6$$

Divide both sides by 2.

$$x=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x=3$$

Substitute 3 for x in the equation \sqrt{x-3}+\sqrt{3-x}=0.

$$\sqrt{3-3}+\sqrt{3-3}=0$$

Simplify. The value x=3 satisfies the equation.

$$0=0$$

Equation \sqrt{x-3}=-\sqrt{3-x} has a unique solution.

$$x=3$$