A symmetric product ratio with a triple-product correction

Proved

WorkbookSource.base_21250

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

lean-workbooksource-checked

Let $a,b,c > 0$ . Show that :

$\frac {(ab + bc + ca)^2}{3abc(a + b + c)} + \frac {abc}{(a + b + c)^3}\ge \frac {28}{27}$

Source: InternLM Lean-Workbook, record lean_workbook_21250 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21250 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * b + b * c + c * a) ^ 2 / (3 * a * b * c * (a + b + c)) + a * b * c / (a + b + c) ^ 3 ≥ 28 / 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21250; Apache-2.0

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