ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 777

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

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

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

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

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

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

\[225 - 2q = 153\]

\[2q = 72\]

\[q = 36\]

\[Ответ:q = 36\text{.\ \ }\]