Problem

Source: Romania National Olympiad 2015, grade x, p.4

Tags: inequalities, algebra, combinatorics, Discrete



Let be a finite set $ A $ of real numbers, and define the sets $ S_{\pm }=\{ x\pm y| x,y\in A \} . $ Show that $ \left| A \right|\cdot\left| S_{-} \right| \le \left| S_{+} \right|^2 . $