Prove2Me

A cyclic mixed squared ratio sum is at least nine quarters

Proved
WorkbookSource.base_28197

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

lean-workbooksource-checked

Prove this inequality with a,b,c are positive a2+2bc(b+c)2+b2+2ca(c+a)2+c2+2ab(a+b)2≥94\frac{a^2+2bc}{(b+c)^2}+\frac{b^2+2ca}{(c+a)^2}+\frac{c^2+2ab}{(a+b)^2}\geq \frac{9}{4}

Source: InternLM Lean-Workbook, record lean_workbook_28197 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_28197 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a^2 + 2 * b * c) / (b + c) ^ 2 + (b^2 + 2 * c * a) / (c + a) ^ 2 + (c^2 + 2 * a * b) / (a + b) ^ 2 ≥ 9 / 4  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28197; Apache-2.0

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