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Sharp inequality

Author: mathforces
Problem has been solved: 9 times

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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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