lean_workbook_plus_40995

Proved

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

Prove that for all real number $x,y,z$ , $(4(x+y+z)-xyz)^2+4(xy+yz+zx-4)^2 \geq 8$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40995 (x y z : ℝ) : (4 * (x + y + z) - x * y * z) ^ 2 + 4 * (x * y + y * z + z * x - 4) ^ 2 ≥ 8   :=  by sorry

Source