6 - Inequalities

Let $a, b, c, x, y, z$ be positive real numbers such that 

$ab + bc + ca = xy + yz + zx = 1$. 

Prove that 

$a(y + z) + b(z + x) + c(x + y) ≥ 2$. 

Proposed by Dorin Andrica, Babes-Bolyai University, Cluj-Napoca, Romania

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