Solve sqrt{3u-5}-sqrt{5u-15}=0

$$\sqrt { 3 u - 5 } - \sqrt { 5 u - 15 } = 0$$

Solve for u

$$u=5$$

Solution Steps

Subtract -\sqrt{5u-15} from both sides of the equation.

$$\sqrt{3u-5}=\sqrt{5u-15}$$

Square both sides of the equation.

$$\left(\sqrt{3u-5}\right)^{2}=\left(\sqrt{5u-15}\right)^{2}$$

Calculate \sqrt{3u-5} to the power of 2 and get 3u-5.

$$3u-5=\left(\sqrt{5u-15}\right)^{2}$$

Calculate \sqrt{5u-15} to the power of 2 and get 5u-15.

$$3u-5=5u-15$$

Subtract 5u from both sides.

$$3u-5-5u=-15$$

Combine 3u and -5u to get -2u.

$$-2u-5=-15$$

Add 5 to both sides.

$$-2u=-15+5$$

Add -15 and 5 to get -10.

$$-2u=-10$$

Divide both sides by -2.

$$u=\frac{-10}{-2}$$

Divide -10 by -2 to get 5.

$$u=5$$

Substitute 5 for u in the equation \sqrt{3u-5}-\sqrt{5u-15}=0.

$$\sqrt{3\times 5-5}-\sqrt{5\times 5-15}=0$$

Simplify. The value u=5 satisfies the equation.

$$0=0$$

Equation \sqrt{3u-5}=\sqrt{5u-15} has a unique solution.

$$u=5$$