Problem
ALG-B2-M02-P002 Product equals 27
#2
★★☆☆☆ Level 2 of 5
Let \(a,b,c>0\) and \(abc=27\). Prove \(a+b+c\ge9\).
Hint 1. Apply AM-GM to \(a,b,c\).
Hint 2. The equality case should give \(a=b=c\).
\(\frac{a+b+c}{3}\ge\sqrt[3]{abc}=3\), hence \(a+b+c\ge9\). Equality occurs when \(a=b=c=3\).
AM-GM module training problem. Method tags: am-gm, fixed-product.