SOLUTION: Solve for x: sqrt(2x-1) - sqrt(x+3) = 1

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Question 65135: Solve for x: sqrt(2x-1) - sqrt(x+3) = 1
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: sqrt(2x-1) - sqrt(x+3) = 1
sqrt%282x-1%29-sqrt%28x%2B3%29%2Bsqrt%28x%2B3%29=sqrt%28x%2B3%29%2B1
sqrt%282x-1%29=sqrt%28x%2B3%29%2B1
%28sqrt%282x-1%29%29%5E2=%28sqrt%28x%2B3%29%2B1%29%5E2
2x-1=sqrt%28%28x%2B3%29%5E2%29%2B2sqrt%28x%2B3%29%2B1
2x-1=x%2B3%2B2sqrt%28x%2B3%29%2B1
2x-1=x%2B4%2B2sqrt%28x%2B3%29
2x-x-1-4=x-x%2B4-4%2B2sqrt%28x%2B3%29
x-5=2sqrt%28x%2B3%29
%28x-5%29%5E2=%282sqrt%28x%2B3%29%29%5E2
x%5E2-10x%2B25=4%28x%2B3%29
x%5E2-10x%2B25=4x%2B12
x%5E2-10x-4x%2B25-12=4x-4x%2B12-12
x%5E2-14x%2B13=0
(x-1)(x-13)=0
x-1=0 or x-13=0
x-1+1=0+1 or x-13+13=0+13
x=1 or x=13 Check for extraneous solutions.
sqrt%282x-1%29-sqrt%28x%2B3%29=1
sqrt%282%281%29-1%29-sqrt%281%2B3%29=1
sqrt%282-1%29-sqrt%284%29=1
sqrt%281%29-sqrt%284%29=1
1-2=1
-1=1 False! x=1 is extraneous!
sqrt%282%2813%29-1%29-sqrt%2813%2B3%29=1
sqrt%2826-1%29-sqrt%2816%29=1
sqrt%2825%29-sqrt%2816%29=1
5-4=1
1=1 True! x=13 is a valid solution!!!
Happy Calculating!!!