SOLUTION: sqrt(x+1)+sqrt(x-1)=sqrt(2x+1)

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Question 991173: sqrt(x+1)+sqrt(x-1)=sqrt(2x+1)
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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sqrt%28x%2B1%29 + sqrt%28x-1%29 = sqrt%282x%2B1%29.

Square both sides:

x+%2B+1 + 2sqrt%28%28x%2B1%29%2A%28x-1%29%29 + x-1 = 2x%2B1.

Simplify:

2x + 2%2Asqrt%28x%5E2-1%29%29 = 2x%2B1,

2%2Asqrt%28x%5E2-1%29 = 1.

Square both sides again:

4%2A%28x%5E2-1%29 = 1.

4x%5E2 = 1+%2B+4 = 5,

x%5E2 = 5%2F4,

x = +/- sqrt%285%29%2F2.

Only positive root suits the original equation  (remember about the term  sqrt%28x-1%29).

Answer.  x = sqrt%285%29%2F2.