SOLUTION: solve. sqrt(2x+7)-sqrt(3x-2)=2

Question 1056659: solve.
sqrt(2x+7)-sqrt(3x-2)=2
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
sqrt(2x+7)-sqrt(3x-2)=2
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sqrt(2x+7) = sqrt(3x-2) + 2
Square both sides.
2x+7 = 3x-2 + 4 + 4sqrt(3x-2)
-x+5 = 4sqrt(3x-2)
Square again
x^2-10x+25 = 16(3x-2) = 48x-32
x^2 - 58x + 57 = 0
(x - 1)*(x - 57) = 0
x = 1
x = 57
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For 57:
sqrt(121) - sqrt(169) = 2 --> not using the principal sqrt.
ie, -11 - (-13) = 2

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