lean_workbook_plus_82031

Proved

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

Let $a,b,c\ge 0$ such that $a + b + c = 3$ . Find the maximum value of: $V = a^3b + b^3c + c^3a$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82031 (a b c V: ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 3) (hV: V = a^3 * b + b^3 * c + c^3 * a): (a = 4/3 ∧ b = 4/3 ∧ c = 4/3 → V = 27 * (4/27)^4) ∧ (a = 4/3 ∧ b = 4/3 ∧ c = 4/3 → ∀ x y z : ℝ, x + y + z = 3 ∧ x^3 * y + y^3 * z + z^3 * x ≤ V)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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