lean_workbook_plus_30300

Disproved

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

For $a,b,c>0$ Prove that: $\sum_{cyc}\frac{a^2}{a^2+ab+b^2}\ge \frac{a+b+c}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30300 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → (a^2/(a^2 + a * b + b^2) + b^2/(b^2 + b * c + c^2) + c^2/(c^2 + c * a + a^2) : ℝ) ≥ (a + b + c) / 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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