Prove2Me

lean_workbook_plus_490

Proved

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

Use another application of AM-GM to prove that 27(a2+b2+c2)(ab+bc+ca)2≥81abc(a+b+c)(a2+b2+c2)27(a^2+b^2+c^2)(ab+bc+ca)^2\geq 81abc(a+b+c)(a^2+b^2+c^2).

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_490 (a b c : ℝ) : 27 * (a ^ 2 + b ^ 2 + c ^ 2) * (a * b + b * c + c * a) ^ 2 ≥ 81 * a * b * c * (a + b + c) * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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