lean_workbook_plus_32407

Proved

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

Without Jensen, prove that if $a,b,c > 0$ , $9(a^3 + b^3 + c^3) \geq (a+b+c)^3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32407 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → 9 * (a^3 + b^3 + c^3) ≥ (a + b + c)^3   :=  by sorry

Source