lean_workbook_plus_82142

Proved

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

proofwiki

Prove that $(x^2y^2+y^2z^2+z^2x^2)^2\geq \frac{(xy+yz+zx)^4}{9}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_82142 (x y z : ℝ) : (x ^ 2 * y ^ 2 + y ^ 2 * z ^ 2 + z ^ 2 * x ^ 2) ^ 2 ≥ (x * y + y * z + z * x) ^ 4 / 9   :=  by sorry

Source