Prove2Me

lean_workbook_plus_29382

Disproved

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

By Holder,

(∑cyca3ab+bc)2(∑cyca(3ab+bc))≥(a+b+c)3\left( \sum_{cyc} \frac{a}{\sqrt{3ab+bc}} \right)^2 \left( \sum_{cyc} a(3ab+bc) \right) \ge (a+b+c)^3

\n\nSo it suffices to show

(a+b+c)3≥94∑cyca(3ab+bc)(a+b+c)^3 \ge \frac 94 \sum_{cyc} a(3ab+bc)
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_29382 : ∀ a b c : ℝ, (a + b + c) ^ 3 ≥ (9 / 4) * (a * (3 * a * b + b * c) + b * (3 * b * c + c * a) + c * (3 * c * a + a * b))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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