lean_workbook_plus_68776

Proved

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

Prove that $3(x^2 + y^2 + z^2)\geq (x + y + z)^2$ using Cauchy-Schwarz inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68776 {x y z : ℝ} : 3 * (x ^ 2 + y ^ 2 + z ^ 2) ≥ (x + y + z) ^ 2   :=  by sorry

Source