lean_workbook_plus_11390

Proved

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

Prove that for positive real numbers a, b, and c, the following inequality holds: \n $(ab+bc+ca) \leq \frac {(a+b+c)^2}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11390 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * b + b * c + c * a) ≤ (a + b + c) ^ 2 / 3   :=  by sorry

Source