A weighted pair-product ratio sum is at least eleven

Proved

WorkbookSource.base_31666

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

lean-workbooksource-checked

Given $a,b,c > 0$ .Prove that: $\frac {20ab}{(a + c)(b + c)} + \frac {15bc}{(b + a)(c + a)} + \frac {12ca}{(c + b)(a + b)} \ge 11$

Source: InternLM Lean-Workbook, record lean_workbook_31666 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31666 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 20 * a * b / (a + c) / (b + c) + 15 * b * c / (b + a) / (c + a) + 12 * c * a / (c + b) / (a + b) ≥ 11  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31666; Apache-2.0

View graph