# How do you solve #sqrt{x + 21} - \sqrt{x - 6} = 3#?

##### 1 Answer

Sep 15, 2016

#### Explanation:

Given:

#sqrt(x+21)-sqrt(x-6) = 3#

Add

#sqrt(x+21) = sqrt(x-6)+3#

Square both sides to get:

#x+21 = (x-6)+6sqrt(x-6)+9 = x+3+6sqrt(x-6)#

Subtract

#18 = 6sqrt(x-6)#

Divide both sides by

#3 = sqrt(x-6)#

Square both sides to get:

#9 = x-6#

Add

#15 = x#

Check the solution

#sqrt(color(blue)(15)+21)-sqrt(color(blue)(15)-6) = sqrt(36)-sqrt(9) = 6 - 3 = 3#