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    OlympiadEasyInequalities10–12

    For positive reals with a+b+c=9a + b + c = 9, what is the largest possible value of abcabc?

    Para reais positivos com a+b+c=9a + b + c = 9, qual é o maior valor possível de abcabc?

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    Solution

    Step 1 of 3

    1. 1.AM-GM gives a+b+c3≥abc3\frac{a+b+c}{3} \ge \sqrt[3]{abc}, so abc3≤3\sqrt[3]{abc} \le 3 and abc≤27abc \le 27.