Problem
ALG-B2-M08-P002 Three ratios
#2
★★☆☆☆ Level 2 of 5
Prove for \(a,b,c>0\): \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge3\).
Hint. Set \(x=a/b\), \(y=b/c\), \(z=c/a\).
Then \(xyz=1\). By AM-GM, \(x+y+z\ge3\sqrt[3]{xyz}=3\), as required.
Teaching goal: recognize the appropriate substitution and check the domain.