lean_workbook_plus_38404

Proved

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

Prove that $(a + b + c)^2 \geq 3(ab + bc + ca)$ using the identity $(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38404 : ∀ a b c : ℝ, (a + b + c) ^ 2 ≥ 3 * (a * b + b * c + c * a)   :=  by sorry

Source