lean_workbook_plus_57513

Proved

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

Let $x;y;z\ge 0$ Prove that $64(x + y + z)^6\ge (x^2 + yz)(y^2 + xz)(z^2 + xy)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57513 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : 64 * (x + y + z) ^ 6 ≥ (x ^ 2 + y * z) * (y ^ 2 + x * z) * (z ^ 2 + x * y)   :=  by sorry

Source

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

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