Problem
ALG-B1-M12-P011 Variant 3, Problem 3
#11
★★★☆☆ Level 3 of 5
If \(a,b,c>0\), \(a+b+c=6\), prove \(abc\le8\).
AM-GM.
\(\sqrt[3]{abc}\le2\), hence \(abc\le8\).
Mock olympiad problem. Tags: am-gm.