SOLUTION: (x+1/x)^2=3 then find the value of x?

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Question 828100: (x+1/x)^2=3 then find the value of x?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(x+1/x)^2=3 then find the value of x?
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%28x%2B1%29%5E2%2Fx%5E2+=+3
%28x%2B1%29%5E2+=+3x%5E2
x%5E2+%2B+2x+%2B+1+=+3x%5E2
2x%5E2+-+2x+-+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-2x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A2%2A-1=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C2+=+1.36602540378444
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C2+=+-0.366025403784439

Quadratic expression 2x%5E2%2B-2x%2B-1 can be factored:
2x%5E2%2B-2x%2B-1+=+%28x-1.36602540378444%29%2A%28x--0.366025403784439%29
Again, the answer is: 1.36602540378444, -0.366025403784439. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-2%2Ax%2B-1+%29