Solve sqrt{9v-15}=sqrt{7v-1}

$$\sqrt { 9 v - 15 } = \sqrt { 7 v - 1 }$$

Solve for v

$$v=7$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{9v-15}\right)^{2}=\left(\sqrt{7v-1}\right)^{2}$$

Calculate \sqrt{9v-15} to the power of 2 and get 9v-15.

$$9v-15=\left(\sqrt{7v-1}\right)^{2}$$

Calculate \sqrt{7v-1} to the power of 2 and get 7v-1.

$$9v-15=7v-1$$

Subtract 7v from both sides.

$$9v-15-7v=-1$$

Combine 9v and -7v to get 2v.

$$2v-15=-1$$

Add 15 to both sides.

$$2v=-1+15$$

Add -1 and 15 to get 14.

$$2v=14$$

Divide both sides by 2.

$$v=\frac{14}{2}$$

Divide 14 by 2 to get 7.

$$v=7$$

Substitute 7 for v in the equation \sqrt{9v-15}=\sqrt{7v-1}.

$$\sqrt{9\times 7-15}=\sqrt{7\times 7-1}$$

Simplify. The value v=7 satisfies the equation.

$$4\times 3^{\frac{1}{2}}=4\times 3^{\frac{1}{2}}$$

Equation \sqrt{9v-15}=\sqrt{7v-1} has a unique solution.

$$v=7$$