Solve sqrt{7u-2}=sqrt{4u+10}

$$\sqrt { 7 u - 2 } = \sqrt { 4 u + 10 }$$

Solve for u

$$u=4$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{7u-2}\right)^{2}=\left(\sqrt{4u+10}\right)^{2}$$

Calculate \sqrt{7u-2} to the power of 2 and get 7u-2.

$$7u-2=\left(\sqrt{4u+10}\right)^{2}$$

Calculate \sqrt{4u+10} to the power of 2 and get 4u+10.

$$7u-2=4u+10$$

Subtract 4u from both sides.

$$7u-2-4u=10$$

Combine 7u and -4u to get 3u.

$$3u-2=10$$

Add 2 to both sides.

$$3u=10+2$$

Add 10 and 2 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{7u-2}=\sqrt{4u+10}.

$$\sqrt{7\times 4-2}=\sqrt{4\times 4+10}$$

Simplify. The value u=4 satisfies the equation.

$$26^{\frac{1}{2}}=26^{\frac{1}{2}}$$

Equation \sqrt{7u-2}=\sqrt{4u+10} has a unique solution.

$$u=4$$