lean_workbook_plus_32829

Proved

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

Let $a,\ b\, c$ be positive real numbers. Find the minimum value of \n\n $\sqrt [3]{\frac {(a^{2008} + 2007b^{2008})(b^{2008} + 2007c^{2008})(c^{2008} + 2007a^{2008})}{a^{2008}b^{2008}c^{2008}}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32829 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2008 + 2007 * b^2008) * (b^2008 + 2007 * c^2008) * (c^2008 + 2007 * a^2008) / (a^2008 * b^2008 * c^2008) ≥ 2008   :=  by sorry

Source

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

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