An algebra problem by Aman Banka

Algebra Level 3

If f(x+1x)=x2+1x2f \left(x+\dfrac 1x\right)=x^2+ \dfrac 1{x^2} for all xC x \in \mathbb{C} , then find f(x)f(x) in C\{0} \mathbb{C} \backslash \{ 0 \} .

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