A cyclic quadratic difference ratio sum is nonnegative

Proved

WorkbookSource.base_44075

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

lean-workbooksource-checked

Prove that $\forall a,b,c>0$ we have $\sum\frac{a^2-bc}{b^2+c^2+2a^2} \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_44075 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44075 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 - b * c) / (b^2 + c^2 + 2 * a^2) + (b^2 - c * a) / (c^2 + a^2 + 2 * b^2) + (c^2 - a * b) / (a^2 + b^2 + 2 * c^2) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44075; Apache-2.0

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