A cyclic quadratic difference ratio sum is nonnegative

Proved

WorkbookSource.plus_24054

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

lean-workbooksource-checked

If $a,b,c>0$ then prove that $\frac{a^2-bc}{b+c+2a}+\frac{b^2-ca}{a+c+2b}+\frac{c^2-ab}{a+b+2c}\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_24054 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_24054 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 - b * c) / (b + c + 2 * a) + (b^2 - c * a) / (a + c + 2 * b) + (c^2 - a * b) / (a + b + 2 * c) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_24054; Apache-2.0

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