lean_workbook_plus_69075

Proved

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

Prove that for any real numbers $a, b, c, d$ , the inequality $2(a^2-ab+b^2)(c^2-cd+d^2) \geq a^2c^2+b^2d^2$ holds. Find the conditions for equality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_69075 (a b c d : ℝ) : 2 * (a^2 - a * b + b^2) * (c^2 - c * d + d^2) ≥ a^2 * c^2 + b^2 * d^2   :=  by sorry

Source