Let $a, b, c$ be positive real numbers for which $ab + ac + bc \ge a + b + c$. Prove that $a + b + c \ge 3$.
Source: Czech-Polish-Slovak Junior Match 2013, Team p5 CPSJ
Tags: inequalities, algebra
Let $a, b, c$ be positive real numbers for which $ab + ac + bc \ge a + b + c$. Prove that $a + b + c \ge 3$.