A symmetric quartic-cubic bound at total zero

Proved

WorkbookSource.base_46041

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

lean-workbooksource-checked

Prove that $(ab+bc+ca)^2+9abc\ge 3(ab+bc+ca)$ given $a+b+c=0$ .

Source: InternLM Lean-Workbook, record lean_workbook_46041 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46041 (a b c : ℝ) (h : a + b + c = 0) : (a * b + b * c + c * a) ^ 2 + 9 * a * b * c ≥ 3 * (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46041; Apache-2.0

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