A quartic bound for two squared symmetric forms

Proved

WorkbookSource.base_9087

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for all real numbers $a, b, c$ we have $(a^2+b^2+c^2-2ab-2bc-2ca)^2 + 9(ab+bc+ca)^2 \geq 30abc(a+b+c)$

Source: InternLM Lean-Workbook, record lean_workbook_9087 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9087 (a b c : ℝ) : (a^2+b^2+c^2-2*a*b-2*b*c-2*c*a)^2 + 9*(a*b+b*c+c*a)^2 ≥ 30*a*b*c*(a+b+c)  :=  by sorry

Source