A cyclic squared difference ratio sum is at least six

Proved

WorkbookSource.base_15069

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

lean-workbooksource-checked

Let $a, b, c>0$ . prove that $\frac{(4a-b-c)^2}{c^2+ab}+\frac{(4b-c-a)^2}{a^2+bc}+\frac{(4c-a-b)^2}{b^2+ca}\ge6$

Source: InternLM Lean-Workbook, record lean_workbook_15069 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_15069 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (4 * a - b - c) ^ 2 / (c ^ 2 + a * b) + (4 * b - c - a) ^ 2 / (a ^ 2 + b * c) + (4 * c - a - b) ^ 2 / (b ^ 2 + c * a) ≥ 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15069; Apache-2.0

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