# Sharp inequality

Author: mathforces
Problem has been solved: 10 times

Русский язык | English Language

The sum of non-negative numbers $a, b, c, x, y, z$ is equal to one. Moreover, it is known that $540 (acy + bxz) \ge 1$. For some coprime positive integer numbers $m$ and $n$ it turned out that $\frac{m}{n}$ is the largest possible value of $abc + bcx + cxy + xyz + yza + zab$. Find $m + n$.

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