Conditionate cu produs

[Marius Mainea]

Daca a,b,c>0 si abc=1 atunci

a) \( \frac{a}{b}+\frac{b}{c}+\frac{1}{a}\ge a+b+1 \)

b) \( a+b+c+\frac{2}{3}(\frac{a}{b}+\frac{b}{c}+\frac{c}{a})\ge 2+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \)