Inegalitate cu a, b, c

[alex2008]

Daca \( a,b,c \in [\frac{1}{3};3] \) sa se arate ca :

\( \frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\ge \frac{7}{5} \)

[Marius Mainea]

Daca \( E(a,b,c)=\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a} \) si \( a=\max\{a,b,c\} \) atunci

\( E(a,b,c)\ge E(a,b,\sqrt{ab})\ge \frac{7}{5} \)