MathDB

A4

Part of 2014 Indonesia MO Shortlist

Problems(1)

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

Source: INAMO Shortlist 2014 A4

5/21/2019
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}
algebrainequalitiesthree variable inequality