Решебник по алгебре 9 класс Мерзляк Задание 148

 

\[\boxed{\text{148\ (148).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[По\ теореме\ неравенства\ \]

\[треугольников\ \]

\[(одна\ сторона\ всегда\ меньше\]

\[суммы\ длин\ двух\ \]

\[других\ сторон)\ получаем:\]

\[a < 8 + 14\]

\[a < 22\]

\[a = 21\ (см) - наименьшее\ \]

\[натуральное\ значение.\]

\[Ответ:21\ см.\]

\[\boxed{\mathbf{148.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left| x^{2} + 10x - 4 \right| = 20\]

\[x^{2} + 10x - 4 = 20\]

\[x^{2} + 10x - 24 = 0\]

\[D_{1} = 25 + 24 = 49\]

\[x_{1} = - 5 + 7 = 2;\]

\[x_{2} = - 5 - 7 = - 12.\]

\[x^{2} + 10x - 4 = - 20\]

\[x^{2} + 10x + 16 = 0\]

\[D_{1} = 25 - 16 = 9\]

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

\[x_{2} = - 5 - 3 = - 8.\]

\[Ответ:\ \pm 2;\ - 12;\ - 8.\]

\[2)\ x|x| + 12x - 45 = 0\]

\[x^{2} + 12x - 45 = 0\]

\[D_{1} = 36 + 45 = 81\]

\[x_{1} = - 6 + 9 = 3;\]

\[x_{2} = - 6 - 9 = - 15.\]

\[- x^{2} + 12x - 45 = 0\]

\[x^{2} - 12x + 45 = 0\]

\[D_{1} = 36 - 45 < 0\]

\[нет\ корней.\]

\[Ответ:\ - 15;\ \ 3.\]

\[3)\ \frac{x^{3}}{|x|} - 14x - 15 = 0\]

\[x^{2} - 14x - 15 = 0\]

\[D_{1} = 49 + 15 = 64\]

\[x_{1} = 7 + 8 = 15;\]

\[x_{2} = 7 - 8 = - 1.\]

\[- x^{2} - 14x - 15 = 0\]

\[x^{2} + 14x + 15 = 0\]

\[D_{1} = 49 - 15 = 34\]

\[x = - 7 \pm \sqrt{34}.\]

\[Ответ:\ - 1;15;\ - 7 \pm \sqrt{34}.\]

\[4)\ x^{2} + 4\sqrt{x^{2}} - 12 = 0\]

\[x^{2} + 4|x| - 12 = 0\]

\[x^{2} + 4x - 12 = 0\]

\[D_{1} = 4 + 12 = 16\]

\[x_{1} = - 2 + 4 = 2;\]

\[x_{2} = - 2 - 4 = - 6.\]

\[x^{2} - 4x - 12 = 0\]

\[D_{1} = 4 + 12 = 16\]

\[x_{1} = 2 + 4 = 6;\]

\[x_{2} = 2 - 4 = - 2.\]

\[Ответ:\ \pm 2;\ \pm 6.\]