Solve sqrt{5u+3}=sqrt{2u+15}

$$\sqrt { 5 u + 3 } = \sqrt { 2 u + 15 }$$

Solve for u

$$u=4$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$5u+3=2u+15$$

Subtract 2u from both sides.

$$5u+3-2u=15$$

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

$$3u+3=15$$

Subtract 3 from both sides.

$$3u=15-3$$

Subtract 3 from 15 to get 12.

$$3u=12$$

Divide both sides by 3.

$$u=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$u=4$$

Substitute 4 for u in the equation \sqrt{5u+3}=\sqrt{2u+15}.

$$\sqrt{5\times 4+3}=\sqrt{2\times 4+15}$$

Simplify. The value u=4 satisfies the equation.

$$23^{\frac{1}{2}}=23^{\frac{1}{2}}$$

Equation \sqrt{5u+3}=\sqrt{2u+15} has a unique solution.

$$u=4$$