lean_workbook_plus_69297

Proved

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

Prove that for all positive real numbers $a,b,c$ the following inequality holds: $(a+b+c)\left(\frac1a+\frac1b+\frac1c\right)\ge\frac{2(a^2+b^2+c^2)}{ab+bc+ca}+7$ and determine all cases of equality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69297 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) * (1 / a + 1 / b + 1 / c) ≥ 2 * (a ^ 2 + b ^ 2 + c ^ 2) / (a * b + b * c + a * c) + 7   :=  by sorry

Source

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

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