Can you minimize \(f(a,b,c,d)\)?

Algebra Level 4

\(a,b,c,d\) are non-negative real numbers such that \(ab+bc+cd+da=1\)

The minimum value of \(f(a,b,c,d)\) \(=\) \(\frac{a^{3}}{b+c+d}+\frac{b^{3}}{a+c+d}+\frac{c^{3}}{a+b+d}+\frac{d^{3}}{a+b+c}\) can be expressed in the form \(\frac{p}{q}\) where \(p\) and \(q\) are relatively prime positive integers.