lean_workbook_plus_82052

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $\sum_{cyc} \frac{1}{a^2+3} \leq \frac{3}{4}$ for positive numbers $a$ , $b$ , and $c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82052 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → 1 / (a ^ 2 + 3) + 1 / (b ^ 2 + 3) + 1 / (c ^ 2 + 3) ≤ 3 / 4   :=  by sorry

Source