lean_workbook_plus_30828

Disproved

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

Let $a,b,c\in [\frac{1}{2},2 ]$ , prove or disprove : $9\le(a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\le10 .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30828 : ∀ a b c : ℝ, a ∈ Set.Icc (1 / 2) 2 ∧ b ∈ Set.Icc (1 / 2) 2 ∧ c ∈ Set.Icc (1 / 2) 2 → 9 ≤ (a + b + c) * (1 / a + 1 / b + 1 / c) ∧ (a + b + c) * (1 / a + 1 / b + 1 / c) ≤ 10   :=  by sorry

Source

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

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