lean_workbook_plus_63880

Proved

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

Let $a,b,c >0$ and $\frac{a+b}{c} + \frac{b+c}{a} +\frac{c+a}{b}=\frac{26}{3}.$ Show that

(a + b + c)( ab +bc + ca) \ge \frac{35}{3}abc

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63880 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a + b) / c + (b + c) / a + (c + a) / b = 26 / 3) : (a + b + c) * (a * b + b * c + c * a) ≥ 35 / 3 * a * b * c   :=  by sorry

Source

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

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