Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 388

\[\boxed{\mathbf{388}.}\]

\[x^{3} - 9x^{2} + ax + b = 0;\ \ \]

\[x_{1} = 1;\ \ x_{2} = 5\]

\[P(1) = 1 - 9 + a + b =\]

\[= a + b - 8 = 0.\]

\[P(5) = 125 - 9 \cdot 25 + 5a + b =\]

\[= 5a + b - 100 = 0.\]

\[\left\{ \begin{matrix} a + b = 8\ \ \ \ \ \ \ \\ 5a + b = 100 \\ \end{matrix} \right.\ ( - )\]

\[- 4a = - 92\]

\[a = 23.\]

\[b = 8 - a = 8 - 23 = - 15.\]

\[Получили:\]

\[P(x) = x^{3} - 9x^{2} +\]

\[+ 23x - 15 = 0.\]

\[(x - 1)(x - 5) = x^{2} - x - 5x +\]

\[+ 5 = x^{2} - 6x + 5.\]

\[P(x) =\]

\[= (x - 1)(x - 5)(x - 3) = 0.\]

\[Ответ:x = 3;\ \ a = 23;\ \ \]

\[b = - 15.\]