lean_workbook_plus_22556

Prove that for arbitrary $\alpha, \beta, x, y \in \mathbb{R}$, the following inequality holds: $(2 \alpha ^2 + 2 \alpha \beta + \beta ^2)(2 x ^2 + 2 xy + y ^2) \ge (2 \alpha x + \alpha y + \beta x + \beta y)^2$.