A squared weighted reciprocal sum upper bound

Proved

WorkbookSource.plus_1874

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

lean-workbooksource-checked

Prove that $\frac{1}{(2a + 2b + c)^2} + \frac{1}{(2b + 2c + a)^2} + \frac{1}{(2c + 2a + b)^2}$ $\leq$ $\frac{9}{25(ab+bc+ac)}$ , where $a, b, c$ are real numbers all greater than 0.

Source: InternLM Lean-Workbook, record lean_workbook_plus_1874 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_1874 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (2 * a + 2 * b + c) ^ 2 + 1 / (2 * b + 2 * c + a) ^ 2 + 1 / (2 * c + 2 * a + b) ^ 2) ≤ 9 / (25 * (a * b + b * c + a * c))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_1874; Apache-2.0

View graph