Question 119
Let $a, b, c \gt 0$ be such that $a^{2} \lt 16 b c$, $b^{2} \lt 16 a c$ and $c^{2} \lt 16 a b$. Show that
$$
a^{2} + b^{2} + c^{2} \lt 2(a b + b c + a c)
$$
$$
a^{2} + b^{2} + c^{2} \lt 2(a b + b c + a c)
$$
MathNet 2024-part-02 — 168 problems (EN–VI) Question 119
Math Olympiad Vault · MathNet 2024-part-02 — 168 problems (EN–VI)