A three-variable cubic upper bound at total five

Proved

WorkbookSource.base_38151

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,\,b,\,c$ be positive real numbers such that $a+b+c=5.$ Prove that $a^2b+c^2a+2abc \le 20.$

Source: InternLM Lean-Workbook, record lean_workbook_38151 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38151 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 5) : a^2 * b + c^2 * a + 2 * a * b * c ≤ 20  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38151; Apache-2.0

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