lean_workbook_plus_40812

Proved

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

Prove that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{a^2}{ab} + \frac{b^2}{bc} + \frac{c^2}{ac} \geq \frac{(a+b+c)^2}{ab+bc+ca}$ where $a,b,c > 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40812 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / b + b / c + c / a = a^2 / (a * b) + b^2 / (b * c) + c^2 / (c * a) ∧ a / b + b / c + c / a ≥ (a + b + c)^2 / (a * b + b * c + c * a)   :=  by sorry

Source

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

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