Inca o inegalitate
Posted: Thu Feb 26, 2009 9:54 pm
Demonstrati ca \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{a+b+c}{\sqrt[3]{abc} \).
Din AM-GM
\( LHS=\frac{(2\frac{a}{b}+\frac{b}{c})+(2\frac{b}{c}+\frac{c}{a})+(2\frac{c}{a}+\frac{a}{b})}{3}\ge RHS \)