lean_workbook_plus_45165

Proved

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

Let be $a,b,c>0$ . Show that : \n\n $(a + b + c)\bigg( \frac {1}{a} + \frac {1}{b} + \frac {1}{c}\bigg)\geq 9 + \frac {2((a-b)^2+(b-c)^2+(c-a)^2)}{ab + bc + ca}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45165 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) * (1 / a + 1 / b + 1 / c) ≥ 9 + 2 * ((a - b) ^ 2 + (b - c) ^ 2 + (c - a) ^ 2) / (a * b + b * c + c * a)   :=  by sorry

Source

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

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