A cubic pairwise sum bounds a symmetric triple-product expression

Proved

WorkbookSource.plus_2290

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

lean-workbooksource-checked

Let a,b,c>0 Prove that $5(ab + bc + ca)^3 + 27(abc)^2 \geq 18abc(a + b + c)(ab + bc + ca)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_2290 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_2290 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 5 * (a * b + b * c + c * a)^3 + 27 * (a * b * c)^2 ≥ 18 * a * b * c * (a + b + c) * (a * b + b * c + c * a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_2290; Apache-2.0

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