lean_workbook_plus_81258

Proved

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

Let $x,y,z \geq 0$ ,prove that: $x^2(3y+x)^2+y^2(3z+y)^2-2(x+y)^2y(3z+x)\geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81258 (x y z : ℝ) : x^2 * (3 * y + x)^2 + y^2 * (3 * z + y)^2 - 2 * (x + y)^2 * y * (3 * z + x) ≥ 0   :=  by sorry

Source