Question

a) (a+b)/(1+a+b)
b)(a+b)/c+(b+c)/a+(c+a)/b≥6,∀a,b,c∈(0;+infinit)
c)1/(a+b)+1/(b+c)+1/(c+a)≤1/2(1/a+1/b+1/c),∀a,b,c∈(0;+infinit)

Answer 1

Indicaţii:
b) Foloseşte $\frac ab+\frac ba \ge 2, \forall a,b\ \textgreater \ 0.$
c) Foloseşte AM-HM: $\frac{a+b}{2}\ge \frac{2}{\frac 1a +\frac 1b}.$