A shifted linear reciprocal upper bound

Proved

WorkbookSource.base_48274

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

lean-workbooksource-checked

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

\frac{1}{2a+b+c} +\frac{1}{a+2b+c} +\frac{1}{a+b+2c} \leq \frac{27(a^2+b^2+c^2)}{4(a+b+c) ^3}

Source: InternLM Lean-Workbook, record lean_workbook_48274 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48274 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (2 * a + b + c) + 1 / (a + 2 * b + c) + 1 / (a + b + 2 * c)) ≤ (27 * (a ^ 2 + b ^ 2 + c ^ 2)) / (4 * (a + b + c) ^ 3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48274; Apache-2.0

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