Problem

Source: Iranian Third Round 2020 Algebra exam Problem2

Tags: inequalities



let $a_1,a_2,...,a_n$,$b_1,b_2,...,b_n$,$c_1,c_2,...,c_n$ be real numbers. prove that $$ \sum_{cyc}{ \sqrt{\sum_{i \in \{1,...,n\} }{ (3a_i-b_i-c_i)^2}}} \ge \sum_{cyc}{\sqrt{\sum_{i \in \{1,2,...,n\}}{a_i^2}}}$$