lean_workbook_plus_16518

Proved

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

Prove that $(x^2y^2+y^2z^2+z^2x^2)^2\geq 3x^2y^2z^2(xy+yz+zx)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16518 (x y z : ℝ) :
  (x^2*y^2+y^2*z^2+z^2*x^2)^2 ≥ 3*x^2*y^2*z^2*(x*y+y*z+z*x)   :=  by sorry

Source