lean_workbook_plus_46588

Proved

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

Prove that $xyz+8 \ge 3(xy+yz+zx)$ given $x^3+y^3+z^3 =3$ and $x,y,z >0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46588 (x y z : ℝ) (hx : x > 0 ∧ y > 0 ∧ z > 0) (h : x^3 + y^3 + z^3 = 3) : x*y*z + 8 ≥ 3 * (x*y + y*z + z*x)   :=  by sorry

Source

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

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