RU-ALLRUSSIAN 1981 Problem 22

What is the smallest value of $4 + \mathbf{x}^{2}\mathbf{y}^{4} + \mathbf{x}^{4}\mathbf{y}^{2} - 3\mathbf{x}^{2}\mathbf{y}^{2}$ for real $\mathbf{x}$ , $\mathbf{y}$ ? Show that the polynomial cannot be written as a sum of squares. [Note the candidates did not know calculus.]