Prove2Me

lean_workbook_plus_58432

Disproved

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

a2+b2+c2+ab+bc+ca+2a+b+c≥23(a+b+c)2+2a+b+c≥43(a+b+c)a+b+c=43\frac{a^2+b^2+c^2+ab+bc+ca+2}{a+b+c} \geq \frac{\frac{2}{3}(a+b+c)^2+2}{a+b+c} \geq \frac{\frac{4}{\sqrt{3}}(a+b+c)}{a+b+c}=\frac{4}{\sqrt{3}}

with equality for a=b=c=33a=b=c=\frac{\sqrt{3}}{3}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_58432 : ∀ a b c : ℝ, (a^2 + b^2 + c^2 + a * b + b * c + c * a + 2) / (a + b + c) ≥ (2 / 3 * (a + b + c)^2 + 2) / (a + b + c) ∧ (2 / 3 * (a + b + c)^2 + 2) / (a + b + c) ≥ (4 / Real.sqrt 3 * (a + b + c)) / (a + b + c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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