SOLUTION: If x–y=7 and xy=6 then find the value of x^4+1/x^4

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Question 889919: If x–y=7 and xy=6 then find the value of x^4+1/x^4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If x–y=7 and xy=6 then find the value of x^4+1/x^4
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x–y=7 --> y = x-7
xy=6
x*(x-7) = 6
x^2 - 7x - 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B-6+=+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=%28-7%29%5E2-4%2A1%2A-6=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+73+%29%29%2F2%5C1+=+7.77200187265877
x%5B2%5D+=+%28-%28-7%29-sqrt%28+73+%29%29%2F2%5C1+=+-0.772001872658765

Quadratic expression 1x%5E2%2B-7x%2B-6 can be factored:
1x%5E2%2B-7x%2B-6+=+%28x-7.77200187265877%29%2A%28x--0.772001872658765%29
Again, the answer is: 7.77200187265877, -0.772001872658765. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B-6+%29

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