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verry original of Iran to propose this.

Source: Iranian Third Round 2020 Algebra exam Problem2

November 20, 2020
inequalities

Problem Statement

let a1,a2,...,ana_1,a_2,...,a_n,b1,b2,...,bnb_1,b_2,...,b_n,c1,c2,...,cnc_1,c_2,...,c_n be real numbers. prove that ∑cyc∑i∈{1,...,n}(3ai−bi−ci)2≥∑cyc∑i∈{1,2,...,n}ai2 \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}}}
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