How do you simplify #sqrt(5x-4)-sqrt(x+8)=2#?

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Answer 1 · 2016-09-02T16:04:14

The solution set is #{8}#.

Isolate one of the #sqrt#'s.

#sqrt(5x - 4) = 2 + sqrt(x + 8)#

Square both sides of the equation:

#(sqrt(5x - 4))^2= (2 + sqrt(x + 8))^2#

#5x - 4 = 4 + 4sqrt(x+ 8) + x + 8#

#4x - 16 = 4sqrt(x + 8)#

#4(x - 4) = 4sqrt(x + 8)#

#x - 4 = sqrt(x + 8)#

Square again:

#(x - 4)^2 = (sqrt(x + 8))^2#

#x^2 - 8x + 16 = x + 8#

#x^2 - 9x + 8 = 0#

#(x -8)(x - 1) = 0#

#x = 8 and 1#

Checking in the original equation, you will find that #x = 8# works while #x = 1# is extraneous.

Hopefully this helps!