SOLUTION: How do I solve this equation: {{{ sqrt ( 2x-3 ) - sqrt ( x-2 ) = 1 }}}

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Question 989398: How do I solve this equation:
+sqrt+%28+2x-3+%29+-+sqrt+%28+x-2+%29+=+1+
Found 2 solutions by rothauserc, josgarithmetic:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt ( 2x-3 ) - sqrt ( x-2 ) = 1
add sqrt ( x-2 ) to both sides of =
sqrt ( 2x-3 ) = 1 + sqrt ( x-2 )
square both sides of =
2x-3 = 1 +2sqrt (x-2) + x-2
x-2 = 2sqrt (x-2)
square both sides of =
x^2-4x+4 = 4x -8
x^2 -8x +12 = 0
(x-6)(x-2) = 0
x = 6 or x = 2
**********************************
check the answers in the original equation
1) x = 6
sqrt(2*6-3) - sqrt(6-2) = 1
3 -2 = 1
1 = 1
answer checks
2) x = 2
sqrt(2*2-3) - sqrt(2-2) = 1
1 - 0 = 1
1 = 1

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This solution requires squaring twice.
sqrt%282x-3%29=sqrt%28x-2%29%2B1
2x-3=x-2%2B2sqrt%28x-2%29%2B1
.
.
x-2=2sqrt%28x-2%29
x%5E2-4x%2B4=4%28x-2%29
x%5E2-8x%2B12=0

highlight_green%28%28x-2%29%28x-6%29=0%29

Either x=2 OR x=6.
Either of them will work.