Question 34
Let $a$, $b$, $c$ be positive real numbers such that $a^2 + b^2 + c^2 \lt 2(a + b + c)$. Prove that
$$
3abc \lt 4(a + b + c).
$$
$$
3abc \lt 4(a + b + c).
$$
MathNet 2008-part-02 — 165 problems (EN–VI) Question 34
Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)