lean_workbook_plus_24867

Proved

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

Given 3 reals (not necessarily positive) x, y, z, satisfying the condition $xyz - 3 = x + y + z$ , show that $3(x^2 + y^2 + z^2) \ge x^2y^2z^2 - 6(x + y + z) - 9$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_24867 (x y z : ℝ) (h : x * y * z - 3 = x + y + z) : 3 * (x ^ 2 + y ^ 2 + z ^ 2) ≥ x ^ 2 * y ^ 2 * z ^ 2 - 6 * (x + y + z) - 9   :=  by sorry

Source

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

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