Question

(a +b) (b+c) (a+c) >(sau egal) 8abc

Answer 1

se demonstreaza prin inegalitatea mediilor
Media aritmetica ≥ Media geometrica
(a+b)/2 ≥ √a x √b
(b+c)/2 ≥ √b x √c
(a+c)/2 ≥ √a x √c
(a+b)/2  x (b+c)/2 x (a+c)/2 ≥ √a x√a x √b x √b x √c x√c
(a+b)(b+c)(a+c) ≥ 2 x 2 x 2 x a x b x c
(a+b)(b+c)(a+c) ≥ 8abc