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Equation Magic?!

Algebra Level 3

If $x + \dfrac{1}{x} = 2$ , what can be said about the value of $x^n + \dfrac{1}{x^n}$ for any real number $n \neq 1$ ?

The values are different for certain

n

's. The resulting value must be 2 for the rest of

n

's. The signs of the value 2 alternate.

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by Michael Huang

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