lean_workbook_plus_73813

Proved

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

Let $a,b,c >0$ and $\frac {1}{a} + \frac {1}{b} + \frac {9}{c} = 3.$ Prove that

a + b + c \geq \frac {25}{3}

Equality holds when $a=b=\frac{5}{3},c=5.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73813 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : 1 / a + 1 / b + 9 / c = 3) : a + b + c >= 25 / 3 ∧ (a = 5 / 3 ∧ b = 5 / 3 ∧ c = 5)   :=  by sorry

Source

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

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