lean_workbook_plus_19537

Proved

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

Let $a, b, c > 0$ . Prove, that $8(a^3+b^3+c^3)^2\geq9(a^2+bc)(b^2+ca)(c^2+ab)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19537 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 8 * (a ^ 3 + b ^ 3 + c ^ 3) ^ 2 ≥ 9 * (a ^ 2 + b * c) * (b ^ 2 + c * a) * (c ^ 2 + a * b)   :=  by sorry

Source

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

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