Question

Fie a,b,c numere reale pozitive . Sa se demonstreze ca:
b) $\frac{b+c}{a}$ + $\frac{a+c}{b}$ + $\frac{a+b}{c}$ $\geq$6.

Answer 1

b/a + c/a + a/b + c/b + a/c + b/c $\geq$ 6.
b/a + a/b$\geq$ 2, c/a + a/c $\geq$ 2 , c/b + b/c $\geq$ 2 , oricare ar fi a,b,c ∈ (0 , + infinit) .