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

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Answer 1 · 2016-09-15T19:40:48

#x=15#

Given:

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

Add #sqrt(x-6)# to both sides to get:

#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 #(x+3)# from both sides to get:

#18 = 6sqrt(x-6)#

Divide both sides by #6# to get:

#3 = sqrt(x-6)#

Square both sides to get:

#9 = x-6#

Add #6# to both sides to get:

#15 = x#

Check the solution #x=15# to ensure that it is a solution of the original equation:

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