lean_workbook_plus_43222

Proved

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

Prove that $\sqrt{(x^2 + y^2 + z^2)^3} \geq x^3 + y^3 + z^3 - 3xyz$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43222 (x y z : ℝ) :
  Real.sqrt ((x ^ 2 + y ^ 2 + z ^ 2) ^ 3) ≥ x ^ 3 + y ^ 3 + z ^ 3 - 3 * x * y * z   :=  by sorry

Source