lean_workbook_plus_15267

Proved

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

Prove for any $x,y,z\geq 0$ : \n $8(x^3 + y^3 + z^3)^2 \geq 9(x^2 + yz)(y^2 + zx)(z^2 + xy)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15267 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : 8 * (x ^ 3 + y ^ 3 + z ^ 3) ^ 2 ≥ 9 * (x ^ 2 + y * z) * (y ^ 2 + z * x) * (z ^ 2 + x * y)   :=  by sorry

Source

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

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