Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 223

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\[1)\ \left\lbrack \begin{matrix} x^{2} - 49 < 0 \\ 9 - x^{2} \geq 0\ \ \\ \end{matrix} \right.\ \]

\[x^{2} - 49 < 0\]

\[(x + 7)(x - 7) < 0\]

\[- 7 < x < 7.\]

\[9 - x^{2} \geq 0\]

\[x^{2} - 9 \leq 0\]

\[(x + 3)(x - 3) \leq 0\]

\[- 3 \leq x \leq 3.\]

\[Ответ:x \in ( - 7;7).\]

\[2)\ \left\lbrack \begin{matrix} 2x - 5 \geq x + 1\ \ \ \ \\ x^{2} - 9x + 14 < 0 \\ \end{matrix} \right.\ \ \]

\[2x - 5 \geq x + 1\]

\[x \geq 6.\]

\[x^{2} - 9x + 14 < 0\]

\[x_{1} + x_{2} = 9;\ \ x_{1} \cdot x_{2} = 14\]

\[x_{1} = 7;\ \ x_{2} = 2.\]

\[(x - 2)(x - 7) < 0\]

\[Ответ:\ \ x > 2.\]