Problem
ALG-B2-M09-P003 Minimum sum
#3
★★☆☆☆ Level 2 of 5
Let \(a,b,c>0\), \(abc=8\). Prove \(a+b+c\ge6\).
Hint. The arithmetic mean is at least the geometric mean.
By AM-GM, \(a+b+c\ge3\sqrt[3]{abc}=6\). Equality occurs at \(a=b=c=2\).
Basic problem with a fixed product.