lean_workbook_plus_17338

Proved

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

Let a, b and c be real numbers. Prove that at least one of $(a+b+c)^2 - 9ab, (a+b+c)^2 - 9bc, (a+b+c)^2 - 9ca$ is non-negative

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17338 (a b c : ℝ) : (a+b+c)^2 - 9*a*b >= 0 ∨ (a+b+c)^2 - 9*b*c >= 0 ∨ (a+b+c)^2 - 9*c*a >= 0   :=  by sorry

Source