VN-TST 2021 Problem 4

Let $a,b,c$ are non-negative numbers such that $2(a^2+b^2+c^2)+3(ab+bc+ca)=5(a+b+c)$ then prove that $4(a^2+b^2+c^2)+2(ab+bc+ca)+7abc\le 25$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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