lean_workbook_plus_2845

Proved

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

Prove that if $a, b, c$ are positive real numbers, then $(a+b+c)^2 \geq 3(ab+bc+ca)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2845 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a + b + c) ^ 2 ≥ 3 * (a * b + b * c + a * c)   :=  by sorry

Source