AMO-Bench 2025 Problem 34

Find $C_{\max}$ such that $\forall x, y, z \in \mathbb{R}$ , $f = 1 + |x+y+z| + |xy+yz+zx| + |xyz| \geq C(|x| + |y| + |z|)$

Dataset text AMO-Bench. Open licence.

Show the answer

\frac{3(16+(\sqrt[3]{7+4\sqrt{3}}+\sqrt[3]{7-4\sqrt{3}}-1)^2)}{32(\sqrt[3]{7+4\sqrt{3}}+\sqrt[3]{7-4\sqrt{3}}-1)}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.