lean_workbook_plus_56569

Proved

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

Prove that $81abc(a+b+c)(a^2+b^2+c^2) \leq 27(ab+bc+ca)^2(a^2+b^2+c^2)$ given $a,b,c>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_56569 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 81 * a * b * c * (a + b + c) * (a ^ 2 + b ^ 2 + c ^ 2) ≤ 27 * (a * b + b * c + c * a) ^ 2 * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source

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

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