O inegalitate mai veche

[Claudiu Mindrila]

Daca \( a_{i},\ b_{i}\in\mathbb{R}_{+},\ i=1,\ 2,\ldots,\ n \), atunci are loc inegalitatea \( \prod_{i=1}^{n}\left(a_{i}+b_{i}\right)\ge2^{n}\prod_{i=1}^{n}\sqrt{a_{i}b_{i}}+\left(\prod_{i=1}^{n}\sqrt{a_{i}}-\prod_{i=1}^{n}\sqrt{b_{i}}\right)^{2} \).
Florin Vulpescu-Jalea