Formula_4669

\[\begin{array}{lr}x_{1}^{3}+x_{2}^{3}+x_{3}^{3}+\alpha x_{1} x_{2} x_{3}+x_{4}^{2}+\ldots+x_{n}^{2} & \left(\alpha^{3}+27 \neq 0, \text { тип } P_{8}\right) ; \\x_{1}^{4}+x_{2}^{4}+\alpha x_{1}^{2} x_{2}^{2}+x_{3}^{2}+\ldots+x_{n}^{2} & \left(\alpha^{2} \neq 4, \text { тип } X_{9}\right) ; \\x_{1}^{3}+x_{2}^{6}+\alpha x_{1}^{2} x_{2}^{2}+x_{3}^{2}+\ldots+x_{n}^{2} & \left(4 \alpha^{3}+27 \neq 0, \text { тип } J_{10}\right) .\end{array}\]