Problem

Source: Vietnam TST 2021 P4-Day 2

Tags: inequalities, algebra



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 $4(a^2+b^2+c^2)+2(ab+bc+ca)+7abc\le 25$