A weighted squared reciprocal upper bound

Proved

WorkbookSource.base_27460

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

lean-workbooksource-checked

Let $a,b,c>0$

\frac{1}{(3a+2b+c)^2}+\frac{1}{(3b+2c+a)^2} + \frac{1}{(3c+2a+b)^2} \le \frac{1}{4(ab+bc+ca)}

Source: InternLM Lean-Workbook, record lean_workbook_27460 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27460 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (3 * a + 2 * b + c) ^ 2 + 1 / (3 * b + 2 * c + a) ^ 2 + 1 / (3 * c + 2 * a + b) ^ 2) ≤ 1 / (4 * (a * b + b * c + c * a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27460; Apache-2.0

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