lean_workbook_plus_23932

Proved

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

$a+\sqrt{ab}\le \frac{9}{8}(a+b)\Rightarrow \frac{1}{a}+\frac{2}{a+b}\le \frac{9}{8}(\frac{1}{a}+\frac{1}{b})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_23932 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : a + Real.sqrt (a * b) ≤ (9 / 8) * (a + b) → 1 / a + 2 / (a + b) ≤ (9 / 8) * (1 / a + 1 / b)   :=  by sorry

Source

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

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