Решебник по алгебре 9 класс Мерзляк Задание 149

 

\[\boxed{\text{149\ (149).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[Пусть\ наши\ последовательные\ \]

\[четные\ числа:x,\ x + 2,\ x + 4.\]

\[Известно,\ что\ их\ сумма\ не\ \]

\[более\ 85.\]

\[Составим\ неравенство:\]

\[x + x + 2 + x + 4 \geq 85\]

\[3x + 6 \geq 85\]

\[3x \geq 79\]

\[x \geq 26\frac{1}{3}\]

\[x = 28 - наименьшее\ \]

\[натуральное\ четное\ число.\]

\[Получаем\ числа:28,\ 30,\ 32.\]

\[Ответ:28,\ 30,\ 32.\]

\[\boxed{\mathbf{149.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left( x^{2} - 2 \right)^{2} - 8 \cdot \left( x^{2} - 2 \right) + 7 =\]

\[= 0\]

\[\left\{ \begin{matrix} x^{2} - 2 = t\ \ \ \ \ \ \ \ \\ t^{2} - 8t + 7 = 0 \\ \end{matrix} \right.\ \]

\[t_{1} + t_{2} = 8,\ \ t_{1} \cdot t_{2} = 7,\ \ \]

\[t_{1} = 7,\ \ t_{2} = 1\]

\[Ответ:\ x = \pm 3;\ x = \pm \sqrt{3}.\]

\[\left\{ \begin{matrix} x^{2} + 5x = t\ \ \ \ \ \ \ \ \\ t² - 2t - 24 = 0 \\ \end{matrix} \right.\ \]

\[t_{1} + t_{2} = 2,\ \ t_{1} \cdot t_{2} = - 24,\ \ \]

\[t_{1} = 6,\ \ t_{2} = - 4\]

\[Ответ:\ x = - 6;\ x = - 4;x = 1;\ \]

\[x = - 1.\]

\[3)\ \left( x^{2} - 3x + 1 \right)\left( x^{2} - 3x + 3 \right) =\]

\[= 3\]

\[\left\{ \begin{matrix} x² - 3x + 1 = t \\ t(t + 2) - 3 = 0 \\ \end{matrix} \right.\ \]

\[t^{2} + 2t - 3 = 0\]

\[t_{1} + t_{2} = - 2,\ \ t_{1} \cdot t_{2} = - 3,\ \ \]

\[t_{1} = - 3,\ \ t_{2} = 1\]

\[\ x_{1} + x_{2} = 3,\ \ x_{1}x_{2} = 4\ \]

\[нет\ корней.\]

\[x(x - 3) = 0\]

\[x = 0,\ \ x = 3\]

\[Ответ:x = 0;x = 3.\]

\[4)\ \left( x^{2} + 2x + 2 \right)\left( x^{2} + 2x - 4 \right) =\]

\[= - 5\]

\[\left\{ \begin{matrix} x^{2} + 2x + 2 = t \\ t(t - 6) + 5 = 0 \\ \end{matrix} \right.\ \]

\[t^{2} - 6t + 5 = 0\]

\[t_{1} + t_{2} = 6,\ \ t_{1} \cdot t_{2} = 5,\ \]

\[\ t_{1} = 5,\ \ t_{2} = 1\]

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

\[x_{1} = - 3,\ \ x_{2} = 1\]

\[Ответ:\ x = - 1;x = 1;\ x = - 3.\]