Question 153
Let $a$, $b$ and $c$ be positive real numbers satisfying $a+b+c \geq a b c$. Prove that
$$
a^{2}+b^{2}+c^{2} \geq \sqrt{3} a b c
$$
$$
a^{2}+b^{2}+c^{2} \geq \sqrt{3} a b c
$$
MathNet 2009-part-02 — 175 problems (EN–VI) Question 153
Math Olympiad Vault · MathNet 2009-part-02 — 175 problems (EN–VI)