lean_workbook_plus_71089

Proved

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

Prove that if $a+b+c=3$ , then $a^3+b^3+c^3-3abc \geq \frac94 (a^2+b^2-2ab)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_71089 (a b c : ℝ) (h : a + b + c = 3) : a^3 + b^3 + c^3 - 3 * a * b * c ≥ (9 / 4) * (a^2 + b^2 - 2 * a * b)   :=  by sorry

Source