A squared pair-product sum with a constant correction

Proved

WorkbookSource.plus_74674

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

lean-workbooksource-checked

Prove that $(ab+bc+ca)^2+9 \ge 18abc$ given $a+b+c=3$ and $a, b, c \in \mathbb{R}$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_74674 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_74674 (a b c : ℝ) (hab : a + b + c = 3) : (a * b + b * c + c * a) ^ 2 + 9 ≥ 18 * a * b * c   :=  by sorry

Source