SOLUTION: Solve square root of 2x+3- square root of x+1=1

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Question 606659: Solve square root of 2x+3- square root of x+1=1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve square root of 2x+3- square root of x+1=1
:
sqrt%282x%2B3%29-sqrt%28x%2B1%29+=+1
:
sqrt%282x%2B3%29+=+sqrt%28x%2B1%29+%2B+1
Square both sides, you have to FOIL the right side
2x + 3 = %28x%2B1%29+%2B+2sqrt%28x%2B1%29+%2B+1
:
2x + 3 = x + 2 + 2sqrt%28x%2B1%29
:
2x - x + 3 - 2 = 2sqrt%28x%2B1%29
:
(x + 1) = 2sqrt%28x%2B1%29
:
Square both sides, FOIL the left side
:
x^2 + 2x + 1 = 4(x+1)
x^2 + 2x + 1 = 4x + 4
x^2 + 2x - 4x + 1 - 4 = 0
x^2 - 2x - 3 = 0
Factors to
(x-3)(x+1) = 0
Two solutions
x = 3
x = -1
;
We have to check both solutions in the original equation
x = -1 will not work, it would give us a neg value inside the radical
Try x = 3
sqrt%286%2B3%29-sqrt%283%2B1%29+=+1; looks OK, x=3 is our solution