Solve sqrt{10-k}=sqrt{3k-6}

$$\sqrt { 10 - k } = \sqrt { 3 k - 6 }$$

Solve for k

$$k=4$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{10-k}\right)^{2}=\left(\sqrt{3k-6}\right)^{2}$$

Calculate \sqrt{10-k} to the power of 2 and get 10-k.

$$10-k=\left(\sqrt{3k-6}\right)^{2}$$

Calculate \sqrt{3k-6} to the power of 2 and get 3k-6.

$$10-k=3k-6$$

Subtract 3k from both sides.

$$10-k-3k=-6$$

Combine -k and -3k to get -4k.

$$10-4k=-6$$

Subtract 10 from both sides.

$$-4k=-6-10$$

Subtract 10 from -6 to get -16.

$$-4k=-16$$

Divide both sides by -4.

$$k=\frac{-16}{-4}$$

Divide -16 by -4 to get 4.

$$k=4$$

Substitute 4 for k in the equation \sqrt{10-k}=\sqrt{3k-6}.

$$\sqrt{10-4}=\sqrt{3\times 4-6}$$

Simplify. The value k=4 satisfies the equation.

$$6^{\frac{1}{2}}=6^{\frac{1}{2}}$$

Equation \sqrt{10-k}=\sqrt{3k-6} has a unique solution.

$$k=4$$