lean_workbook_plus_71322

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a, b$ be positive numbers. Prove that

\frac{1}{a+2b}+\frac{1}{b+2a}\leq \frac{2}{3\sqrt{ab}}.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_71322 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (1 / (a + 2 * b) + 1 / (b + 2 * a) ≤ 2 / (3 * Real.sqrt (a * b)))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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