lean_workbook_plus_49560

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $(ab+bc+ca-3)^2 \ge 9(abc-1)$ given $a+b+c=3$ and $a, b, c \in \mathbb{R}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49560 (a b c : ℝ) (ha : a + b + c = 3) : (a * b + b * c + c * a - 3) ^ 2 ≥ 9 * (a * b * c - 1)   :=  by sorry

Source