A normalized cubic sum with a symmetric reciprocal correction

Proved

WorkbookSource.base_9732

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Given $a,b,c>0$ show that :

$\frac{a^3+b^3+c^3}{3abc}+\frac{9abc}{(a+b+c)(ab+bc+ca)}\ge 2$

Source: InternLM Lean-Workbook, record lean_workbook_9732 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9732 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :  (a^3 + b^3 + c^3) / (3 * a * b * c) + (9 * a * b * c) / ((a + b + c) * (a * b + b * c + c * a)) ≥ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9732; Apache-2.0

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