# How do you solve sqrt(3k-11)=sqrt(5-k)?

Feb 12, 2017

$k = 4$

#### Explanation:

Given:

$\sqrt{3 k - 11} = \sqrt{5 - k}$

Square both sides (noting that this may introduce an extraneous solution) to get:

$3 k - 11 = 5 - k$

Add $11 + k$ to both sides to get:

$4 k = 16$

Divide both sides by $4$ to get:

$k = 4$

Check:

$\sqrt{3 \cdot \textcolor{b l u e}{4} - 11} = \sqrt{1} = \sqrt{5 - \textcolor{b l u e}{4}}$