lean_workbook_plus_50417

Proved

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

Let a,b,c >0 satisfy $(1+\frac{a}{b})(1+\frac{b}{c})(1+\frac{c}{a}) = 9$ . Show that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{10}{a+b+c}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50417 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 + a / b) * (1 + b / c) * (1 + c / a) = 9 → 1 / a + 1 / b + 1 / c = 10 / (a + b + c)   :=  by sorry

Source

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

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