SOLUTION: Suppose a and x satisfy x^2 + x(a-(1/a)) - 1 = 0. Solve for x in terms of a.

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Question 1022832: Suppose a and x satisfy x^2 + x(a-(1/a)) - 1 = 0. Solve for x in terms of a.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + x(a-(1/a)) - 1 = 0

x%5E2%2Bx%28a-%281%2Fa%29%29-1=0

x%5E2%2Bx%28a%5E2-1%29%2Fa-1=0

Use general solution for a quadratic equation.
x=%28-%28a%5E2-1%29%2Fa%2B-+sqrt%28%28%28a%5E2-1%29%2Fa%29%5E2-4%28-1%29%29%29%2F2

x=%28-%28a%5E2-1%29%2Fa%2B-+sqrt%28%28%28a%5E2-1%29%2Fa%29%5E2%2B4%29%29%2F2------------this may be still further simplifiable.