SOLUTION: square root(2x-1) - square root(x+3) = 1 solve

Question 94296: square root(2x-1) - square root(x+3) = 1
solve
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
square root(2x-1) - square root(x+3) = 1
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Square both sides to get:
(2x-1) -2sqrt[(2x-1)(x+3)]+(x+3) = 1
Simplify:
-2sqrt[2x^2+5x-3)] = -3x-1
Square both sides to get:
4(2x^2+5x-3) = 9x^2+6x+1
Simplify:
x^2-14x+13 = 0
(x-1)(x-13)=0
x = 1 or x=13
Checking for extraneous roots in "square root(2x-1) - square root(x+3) = 1":
If x = 1: sqrt(1) - sqrt(4) = 1
1-2 = 1
Wrong, so x=1 is not a solution of the orignial equation.
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If x= 13 : sqrt(25) - sqrt(16) = 1
5-4 = 1
True, so x=13 is the final solution.
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Cheers,
Stan H.

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