An algebra problem by Aman Banka

Algebra Level pending

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

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