lean_workbook_plus_14455

Proved

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

The following inequality is also true. Let $a,b,c$ be positive numbers . Show that $(a+b+c)(\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c})\ge 2+\frac{7(b+c)(c+a)(a+b)}{8abc}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14455 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) * (1 / a + 1 / b + 1 / c) ≥ 2 + (7 * (b + c) * (c + a) * (a + b)) / (8 * a * b * c)   :=  by sorry

Source

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

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