A weighted cyclic linear ratio sum is at least eight

Proved

WorkbookSource.plus_73378

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

lean-workbooksource-checked

Let $a, b, c$ be positive real numbers. Prove o disprove that

$\frac{5a + 3c}{2a + b} + \frac{5b + 3a}{2b + c} + \frac{5c + 3b}{2c + a} \ge 8$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_73378 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_73378 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (5 * a + 3 * c) / (2 * a + b) + (5 * b + 3 * a) / (2 * b + c) + (5 * c + 3 * b) / (2 * c + a) ≥ 8   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_73378; Apache-2.0

View graph