lean_workbook_plus_69671

Proved

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

If $x,y,z$ are real numbers, then \n\n $x^4+y^4+z^4+(xy+yz+zx)(x^2+y^2+z^2)\ge4xyz(x+y+z).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69671 (x y z : ℝ) : x^4 + y^4 + z^4 + (x*y + y*z + z*x)*(x^2 + y^2 + z^2) ≥ 4*x*y*z*(x + y + z)   :=  by sorry

Source