lean_workbook_plus_5177

Proved

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

Show that for positive real numbers a, b, and c, the following inequality holds:\n $a^3+b^3+c^3+24abc\le(a+b+c)^3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_5177 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + 24 * a * b * c ≤ (a + b + c)^3   :=  by sorry

Source