ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 283

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\[1)\log_{6}\left( 49 - x^{2} \right)\]

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

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

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

\[- 7 < x < 7\]

\[Ответ:\ - 7 < x < 7.\]

\[2)\log_{7}\left( x^{2} + x - 6 \right)\]

\[x^{2} + x - 6 > 0\]

\[D = 1^{2} + 4 \bullet 6 = 1 + 24 = 25\]

\[x_{1} = \frac{- 1 - 5}{2} = - 3;\text{\ \ }\]

\[x_{2} = \frac{- 1 + 5}{2} = 2.\]

\[(x + 3)(x - 2) > 0\]

\[x < - 3\ \ и\ \ x > 2\]

\[Ответ:\ \ x < - 3;\ \ x > 2.\]

\[3)\log_{\frac{1}{5}}\left( x^{2} + 2x + 7 \right)\]

\[x^{2} + 2x + 7 > 0\]

\[D = 2^{2} - 4 \bullet 7 = 4 - 28 =\]

\[= - 24 < 0\]

\[a = 1 > 0\]

\[x - любое\ число\]

\[Ответ:\ \ при\ любом\ \text{x.}\]