lean_workbook_plus_25229

Proved

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

Let $x, y \geq 0.$ Prove that $x^2+xy+y^2 \leq 3(x- \sqrt{xy}+y)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25229 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) : x^2 + x*y + y^2 ≤ 3 * (x - Real.sqrt (x*y) + y)^2   :=  by sorry

Source