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## the least value for :$\frac{a}{b^3+54}+\frac{b}{c^3+54}+\frac{c}{a^3+54}$

For every $a,b,c$ non-negative real number such that:$a+b+c=1$ how to find the least value for :

$$\frac{a}{b^3+54}+\frac{b}{c^3+54}+\frac{c}{a^3+54}$$

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Curious looking question. Where did you find it? – Yemon Choi Jan 13 at 10:16
It is a question to train for olympic level,i suppose . – tiv Jan 13 at 10:27
Why not ask this problem on an Olympiad website rather than here? e.g. art of problem solving? It would be far more appropriate there. – wccanard Jan 13 at 11:58