SE-SKOLORNAS 2017 Problem 6

Let $a,b,c,x,y,z$ be real numbers such that $x+y+z=0$ , $a+b+c\geq 0$ , $ab+bc+ca \ge 0$ . Prove that $ax^2+by^2+cz^2\ge 0$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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