lean_workbook_plus_77706

import Mathlib.Analysis.Complex.Basic

theorem lean_workbook_plus_77706 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : (x + 2 * y + z) * (y + 2 * z + x) * (z + 2 * x + y) ≥ (3 * x + z) * (3 * y + x) * (3 * z + y)   :=  by sorry