SOLUTION: sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions)

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Question 62139: sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions)
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(2x+3) - sqrt(x+1) = 1, solve for x ( could be 2 solutions)
sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+1.
sqrt%282x%2B3%29+=+1%2Bsqrt%28x%2B1%29.
Square both sides:
2x%2B3+=+1+%2B+2sqrt%28x%2B1%29+%2B+x%2B1.
Combine like terms:
x%2B1+=+2sqrt%28x%2B1%29.
Square both sides again:
x%5E2%2B2x%2B1+=+4%28x%2B1%29+=+4x%2B4.
Turn this into the form of a quadratic equation:
x%5E2+-+2x+-+3+=+0+.
This equation factors: %28x%2B1%29%28x-3%29.
So, x+=+-1 or x+=+3.
Let's verify these answers:
When x = -1 then sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+sqrt%281%29+-+sqrt%280%29+=+1.
When x = 3 then sqrt%282x%2B3%29+-+sqrt%28x%2B1%29+=+sqrt%289%29+-+sqrt%284%29+=+3+-+2+=+1.