lean_workbook_plus_14709

Proved

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

Let $a, b, c>0$ and $(a+b) (b+c) =4$ . Prove that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{b}{ca} \geq \frac{27}{8}$ (Found by WolframAlpha)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14709 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a + b) * (b + c) = 4) : 1 / a + 1 / b + 1 / c + b / (c * a) ≥ 27 / 8   :=  by sorry

Source

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

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