Question 63
Given positive real numbers $a$, $b$, $c$, with $ab + bc + ca \ge a + b + c$, prove that
$$(a+b+c)(ab+bc+ca) + 3abc \ge 4(ab+bc+ca).$$
(I. Gorodnin)
$$(a+b+c)(ab+bc+ca) + 3abc \ge 4(ab+bc+ca).$$
(I. Gorodnin)
Math Olympiad Vault · MathNet 2014