lean_workbook_plus_61330

Proved

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

Prove that for all real numbers $x,y,z$ the following inequality holds: $x^2+y^2+z^2-xy-yz-xz \ge \frac{3}{4}(x-y)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61330 (x y z: ℝ) : x ^ 2 + y ^ 2 + z ^ 2 - x * y - y * z - x * z ≥ 3 / 4 * (x - y) ^ 2   :=  by sorry

Source