Prove2Me

lean_workbook_plus_9855

Proved

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

Prove for a,b>0a,b>0 : 2aa+b+b2a≥12(a−ba+b)2\frac{2a}{a+b}+\frac{b}{2a}\ge \frac{1}{2}\left(\frac{a-b}{a+b}\right)^{2}

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_9855 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (2 * a / (a + b) + b / (2 * a)) ≥ 1 / 2 * ((a - b) / (a + b)) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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