Minimum Value

Calculus Level 3

\[\large f(x)=\frac{(x+1/x)^{6}-(x^{6}+1/x^{6})-2}{(x+1/x)^{3}+(x^{3}+1/x^{3})}\]

Find the minimum value of \(f(x)\) above for real \(x>0\).


Problem Source: Putnam (1998)
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