Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 457

\[1)\ C_{x}^{2} + C_{x}^{3} = 15(x - 1)\]

\[C_{x + 1}^{3} = 15(x - 1)\]

\[\frac{(x + 1)!}{3!(x - 2)!} = 15(x - 1)\]

\[\frac{(x + 1)x(x - 1)(x - 2)!}{3 \bullet 2 \bullet (x - 2)!} = 15(x - 1)\]

\[(x + 1)x = 15 \bullet 6\]

\[x^{2} + x - 90 = 0\]

\[D = 1 + 360 = 361\]

\[x_{1} = \frac{- 1 - 19}{2} = - 10;\text{\ \ }\]

\[x_{2} = \frac{- 1 + 19}{2} = 9.\]

\[Ответ:\ \ 9.\]

\[2)\ C_{x - 1}^{3} + C_{x - 1}^{2} = 15(x - 2)\]

\[C_{x}^{3} = 15(x - 2)\]

\[\frac{x!}{3!(x - 3)!} = 15(x - 2)\]

\[\frac{x(x - 1)(x - 2)(x - 3)!}{3 \bullet 2 \bullet (x - 3)!} = 15(x - 2)\]

\[x(x - 1) = 15 \bullet 6\]

\[x^{2} - x - 90 = 0\]

\[D = 1 + 360 = 361\]

\[x_{1} = \frac{1 - 19}{2} = - 9;\text{\ \ }\]

\[x_{2} = \frac{1 + 19}{2} = 10.\]

\[Ответ:\ \ 10.\]