lean_workbook_plus_66590

Disproved

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

Let $a=\frac{1}{x},b=\frac{1}{y},c=\frac{1}{z}$ . Then using $xyz=1$ , our inequality is equivalent to $\frac{9}{2}\le \sum\frac{x}{y+z}\cdot \sum x\le 3\sum \frac{x^{2}}{y+z}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66590 :
  ∀ x y z : ℝ, 1 / x * 1 / y * 1 / z = 1 → 9 / 2 ≤ (1 / x + 1 / y + 1 / z) * (x + y + z) ∧ (1 / x + 1 / y + 1 / z) * (x + y + z) ≤ 3 * (1 / x * x + 1 / y * y + 1 / z * z)   :=  by sorry

Source

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

View graph