lean_workbook_plus_25467

Proved

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

Let $a ,b ,c>0$ and $\frac{b+c}{a}+ \frac{c+a}{b}=9.$ Prove that

(a+b+c)\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right) \geq \dfrac{88}{7}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25467 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (b + c) / a + (c + a) / b = 9) :
  (a + b + c) * (1 / a + 1 / b + 1 / c) ≥ 88 / 7   :=  by sorry

Source

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

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