A weighted cyclic reciprocal sum with a symmetric quadratic correction

Proved

WorkbookSource.base_28673

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove:

\frac{a+2b}{c}+\frac{b+2c}{a}+\frac{c+2a}{b}+\frac{117(ab+bc+ca)}{8(a^2+b^2+c^2)} \ge \frac{89}{4}

Source: InternLM Lean-Workbook, record lean_workbook_28673 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28673 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + 2 * b) / c + (b + 2 * c) / a + (c + 2 * a) / b + 117 * (a * b + b * c + c * a) / (8 * (a ^ 2 + b ^ 2 + c ^ 2)) ≥ 89 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28673; Apache-2.0

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