A weighted quadratic reciprocal upper comparison

Proved

WorkbookSource.base_12662

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be positive numbers. Prove that: $(9a^2+9b^2+c^2 )\left(\frac{1}{a+4c}+\frac{1}{b+4c}\right)\geq 2(a+b)$

Source: InternLM Lean-Workbook, record lean_workbook_12662 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12662 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (9 * a ^ 2 + 9 * b ^ 2 + c ^ 2) * (1 / (a + 4 * c) + 1 / (b + 4 * c)) ≥ 2 * (a + b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12662; Apache-2.0

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