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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 147
Задание 147
\[\boxed{\text{147\ (147).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ 5x - яблонь,\ 4x -\]
\[вишен,\ 2x - слив.\ Тогда\ \]
\[всего\ деревьев\ \]
\[5x + 4x + 2x = 11x\text{.\ }\]
\[По\ условию\ задачи\ известно,\ \]
\[что\ деревьев\ не\ менее\ \]
\[120\ штук.\]
\[Составляем\ неравенство:\]
\[11x \geq 120\]
\[x \geq \frac{120}{11}\]
\[x \geq 10\frac{10}{11}\]
\[x = 11 - наименьшее\ \]
\[целое\ число.\]
\[4 \cdot 11 = 44\ (штуки) -\]
\[наименьшее\ количество\ \]
\[вишен.\]
\[Ответ:44\ вишни.\]
\[\boxed{\mathbf{147.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \left| x^{2} + 7x - 4 \right| = 4\]
\[x^{2} + 7x - 4 = 4\]
\[x^{2} + 7x - 8 = 0\]
\[x_{1} + x_{2} = - 7;\ \ x_{1} \cdot x_{2} = - 8\]
\[x_{1} = - 8;\ \ \ x_{2} = 1.\]
\[x^{2} + 7x - 4 = - 4\]
\[x^{2} + 7x = 0\]
\[x(x + 7) = 0\]
\[x = 0;\ \ x = - 7.\]
\[Ответ: - 8;\ - 7;\ \ 0;\ \ 1.\]
\[2)\ \ 5x^{2} - 8|x| + 3 = 0\]
\[5x^{2} - 8x + 3 = 0\]
\[D_{1} = 16 - 15 = 1\]
\[x_{1} = \frac{(4 + 1)}{5} = 1;\]
\[x_{2} = \frac{4 - 1}{5} = \frac{3}{5} = 0,6.\]
\[5x^{2} + 8x + 3 = 0\]
\[D_{1} = 16 - 15 = 1\]
\[x_{1} = \frac{- 4 + 1}{5} = - \frac{3}{5} = - 0,6;\]
\[x_{2} = \frac{- 4 - 1}{5} = - 1.\]
\[Ответ:\ \pm 1;\ \pm 0,6.\]
\[3)\ x|x| + 6x - 5 = 0\]
\[x^{2} + 6x - 5 = 0\]
\[D_{1} = 9 + 5 = 14\]
\[x = - 3 \pm \sqrt{14}.\]
\[- x^{2} + 6x - 5 = 0\]
\[x^{2} - 6x + 5 = 0\]
\[D_{1} = 9 - 5 = 4\]
\[x_{1} = 3 + 2 = 5;\]
\[x_{2} = 3 - 2 = 1.\]
\[Ответ:\ - 3 \pm \sqrt{14};\ \ 1;\ \ 5.\]
\[4)\ x^{2} + \frac{4x^{2}}{|x|} - 12 = 0\]
\[x^{2} + 4x - 12 = 0\]
\[D_{1} = 4 + 12 = 16\]
\[x_{1} = - 2 + 4 = 2;\]
\[x_{2} = - 2 - 4 = - 6.\]
\[x^{2} - 4x - 12 = 0\]
\[D_{1} = 4 + 12 = 16\]
\[x_{1} = 2 + 4 = 6;\]
\[x_{2} = 2 - 4 = - 2.\]
\[Ответ:\ \pm 2;\ \pm 6.\]
\[5)\ x^{2} - 8\sqrt{x^{2}} + 15 = 0\]
\[x^{2} - 8|x| + 15 = 0\]
\[x^{2} - 8x + 15 = 0\]
\[D_{1} = 16 - 15 = 1\]
\[x_{1} = 4 + 1 = 5;\]
\[x_{2} = 4 - 1 = 3.\]
\[x^{2} + 8x + 15 = 0\]
\[D_{1} = 16 - 15 = 1\]
\[x_{1} = - 4 + 1 = - 3;\]
\[x_{2} = - 4 - 1 = - 5.\]
\[Ответ:\ \pm 5;\ \pm 3.\]
\[6)\ x^{2} - 8\sqrt{x^{2}} - 9 = 0\]
\[x^{2} - 8|x| - 9 = 0\]
\[x^{2} - 8x - 9 = 0\]
\[D_{1} = 16 + 9 = 25\]
\[x_{1} = 4 + 5 = 9;\]
\[x_{2} = 4 - 5 = - 1.\]
\[x^{2} + 8x - 9 = 0\]
\[D_{1} = 16 + 9 = 25\]
\[x_{1} = - 4 + 5 = 1;\]
\[x_{2} = - 4 - 5 = - 9.\]
\[Ответ: \pm 9;\ \pm 1.\]
