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(a+b+c)/5 <= \sqrt[3]{abc} if 1 <= a, b, c <= 8

Source: INAMO Shortlist 2014 A4

May 21, 2019
algebrainequalitiesthree variable inequality

Problem Statement

Prove that for every real positive number a,b,ca, b, c with 1≤a,b,c≤81 \le a, b, c \le 8 the inequality a+b+c5≤abc3\frac{a+b+c}{5}\le \sqrt[3]{abc}
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