Prove2Me

lean_workbook_plus_73957

Proved

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

Let a,b a,b are positve reals such that a+2b=1. a+2b=1. Prove that (a+1b)(b+1a)≥818 (a+\frac{1}{b})(b+\frac{1}{a})\geq \frac{81}{8} Equality holds when a=12,b=14.a=\frac{1}{2},b=\frac{1}{4}.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_73957 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + 2 * b = 1) : (a + 1 / b) * (b + 1 / a) ≥ 81 / 8   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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