SOLUTION: Help me please to solve this problem If {{{ x^2 - 5x - 1 = 0 }}}, what is the value of {{{ x^2 + 1/x^2 }}}?

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Question 1044047: Help me please to solve this problem
If +x%5E2+-+5x+-+1+=+0+, what is the value of +x%5E2+%2B+1%2Fx%5E2+?
Found 2 solutions by josgarithmetic, robertb:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the quadratic equation either by Completing The Square or directly using general formula for solution of quadratic equation; and then substitute the result in the requested expression.


system%28x%5E2%2Bbx%2Bc=0%2Cx=%28-b%2B-+sqrt%28b%5E2-4c%29%29%2F2%29

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let alpha be a root of this quadratic equation. Then its conjugate is also a root, which is given by -1%2Falpha.
===> alpha+-+1%2Falpha+=+5, by property of the coefficient of x...

===> alpha%5E2+-+2+%2B+1%2Falpha%5E2+=+25, after squaring both sides...

===> alpha%5E2+%2B+1%2Falpha%5E2+=+27