SOLUTION: Please help with this problem: sqrt(2x+3) + sqrt(x-2) =2

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Question 870032: Please help with this problem:
sqrt(2x+3) + sqrt(x-2) =2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I don't this can have a solution, but let's see.
:
sqrt%282x%2B3%29+%2B+sqrt%28x-2%29+=+2
subtrac sqrt(x-2) from both sides
sqrt%282x%2B3%29+=+2+-+sqrt%28x-2%29
Square both sides, the right side needs to be FOILed
%282x%2B3%29+=+4+-+4sqrt%28x-2%29%2B+%28x-2%29
%282x%2B3%29+=+x+%2B+4+-+2+-+4sqrt%28x-2%29%29
%282x%2B3%29+=+x+%2B+2+-+4sqrt%28x-2%29
combine like terms on the left
2x+-+x+%2B+3+-+2+=+-4sqrt%28x-2%29
%28x+%2B+1%29+=+-4sqrt%28x-2%29
square both sides again, the left side is FOILed
x%5E2+%2B+2x+%2B+1+=+16%28x-2%29
x%5E2+%2B+2x+%2B+1+=+16x+-+32
x^2 + 2x - 16x + 1 + 32 = 0
x^2 - 14x + 33 = 0
Factors to
(x-11)(x-3) = 0
Two solutions
x = 11
x = 3
Try both solutions in the original problem, neither works, so there is no solution