A weighted pairwise product bound at unit sum

Proved

WorkbookSource.base_29461

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

lean-workbooksource-checked

a, b and c are positive real numbers such that a+b+c = 1. Prove the following inequality:

$ab + 2bc + 3ac \le \frac{3}{4}$

Source: InternLM Lean-Workbook, record lean_workbook_29461 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29461 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : a * b + 2 * b * c + 3 * a * c ≤ 3 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29461; Apache-2.0

View graph