lean_workbook_plus_49641

Proved

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

Using the AM-GM Inequality, $\frac{(xz)^{2}+(yx)^{2}+(zy)^{2}}{xyz}\geq\frac{(xz)(yx)+(yx)(zy)+(zy)(xz)}{xyz}= x+y+z\,.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49641 (x y z: ℝ) : (x * z) ^ 2 + (y * x) ^ 2 + (z * y) ^ 2 ≥ x * y * z * (x + y + z)   :=  by sorry

Source