lean_workbook_plus_63395

Proved

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

Prove that if $xyz<0$ , then $x^2+y^2+z^2\geq\sqrt{xyz(x+y+z)}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63395 (x y z : ℝ) (h : x * y * z < 0) :
  x^2 + y^2 + z^2 ≥ Real.sqrt (x * y * z * (x + y + z))   :=  by sorry

Source