Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1403

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\[1)\ 5^{x^{2} + 3x + 1,5} < 5\sqrt{5}\]

\[5^{x^{2} + 3x + 1,5} < 5^{1 + \frac{1}{2}}\]

\[x^{2} + 3x + 1,5 < 1,5\]

\[x^{2} + 3x < 0\]

\[(x + 3) \bullet x < 0\]

\[- 3 < x < 0\]

\[Ответ:\ \ - 3 < x < 0.\]

\[2)\ {0,2}^{x^{2} - 6x + 7} \geq 1\]

\[{0,2}^{x^{2} - 6x + 7} \geq {0,2}^{0}\]

\[x^{2} - 6x + 7 \leq 0\]

\[D = 36 - 28 = 8 = 4 \bullet 2\]

\[x = \frac{6 \pm \sqrt{8}}{2} = \frac{6 \pm 2\sqrt{2}}{2} =\]

\[= 3 \pm \sqrt{2};\]

\[\left( x - \left( 3 - \sqrt{2} \right) \right)\left( x + \left( 3 - \sqrt{2} \right) \right) \geq 0\]

\[3 - \sqrt{2} < x < 3 + \sqrt{2}.\]

\[Ответ:\ \ 3 - \sqrt{2} < x < 3 + \sqrt{2}.\]

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