[tex]\Delta = \left|\begin{array}{ccc}x_1&x_2&x_3\\x_2&x_3&x_1\\x_3&x_1&x_2\end{array}\right| = \\ \\ =x_1x_3x_2+x_1x_2x_3+x_1x_2x_3 - x_1^3-x_2^3-x_3^3= \\ \\ = 3x_1x_2x_3-(x_1^3+x_2^3+x_3^3)\\ \\ x^3-x=0 \Rightarrow x^3 = x \Rightarrow x_k^3 = x_k,\quad k = \overline{1,3} \\ \\ \Delta = 3\cdot 0 - (x_1+x_2+x_3) = 0-0 = 0[/tex]
