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

Algebra Level 3

$$a,b,c,d$$ 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.

Find the value of $$p+q$$

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