lean_workbook_plus_50568

Proved

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

Let $u=\sqrt{x}$ , then it is $2u^3+y^3\ge 3u^2y\iff (u-y)^2(2u+y)\ge 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_50568 (x y : ℝ) : 2 * (Real.sqrt x) ^ 3 + y ^ 3 ≥ 3 * (Real.sqrt x) ^ 2 * y ↔ (Real.sqrt x - y) ^ 2 * (2 * Real.sqrt x + y) ≥ 0   :=  by sorry

Source

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

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