ГДЗ по алгебре 8 класс Макарычев Задание 684

\[\boxed{\text{684\ (684).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{2} - 15x + q = 0,\]

\[\text{\ \ }x_{1}^{2} + x_{2}^{2} = 153\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = 15 \\ x_{1}x_{2} = q\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]

\[x_{1}^{2} + x_{2}^{2} =\]

\[= x_{1}^{2} + 2x_{1}x_{2} + x_{2}^{2} - 2x_{1}x_{2} =\]

\[= \left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} =\]

\[= 15^{2} - 2q = 153\]

\[225 - 2q = 153\]

\[2q = 72\]

\[q = 36\]

\[Ответ:q = 36\text{.\ \ }\]