Решебник по алгебре 9 класс Мерзляк Задание 858

 

\[\boxed{\mathbf{858\ (858).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x + 6,\ \ \ x + 2,\ \ \ 3x - 4\]

\[(x + 2)^{2} = (x + 6)(3x - 4)\text{\ \ }\]

\[x^{2} + 4x + 4 = 3x^{2} - 4x +\]

\[+ 18x - 24,\]

\[2x² + 10x - 28 = 0\ \ \ \ |\ :2\]

\[x^{2} + 5x - 14 = 0\]

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

\[x_{1}x_{2} = - 14;\ x_{2} = 2\]

\[при\ x = - 7:\ \ \]

\[- 7 + 6 = - 1,\ \ - 7 + 2 = - 5,\]

\[\ \ 3 \cdot ( - 7) - 4 = - 25;\]

\[при\ x = 2:\ \ \]

\[2 + 6 = 8,\ \ 2 + 2 = 4,\]

\[\ \ 3 \cdot 2 - 4 = 2.\]

\[Ответ:x = - 7 \Longrightarrow \ b =\]

\[= - 1,\ - 5,\ - 25\ \ \ или\ \ \ \]

\[x = 2 \Longrightarrow b = \ 8,\ 4,\ 2.\]

\[\boxed{\mathbf{858.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Сумма\ всех\ двузначных\ чисел:\]

\[S_{0} = \frac{a_{1} + a_{n}}{2} \cdot n =\]

\[= \frac{10 + 99}{2} \cdot 90 =\]

\[= 109 \cdot 45 = 4905\]

\[Числа,\ кратные\ 3:\]

\[a_{n} = a_{1} + d(n - 1),\]

\[\ \ 99 = 12 + 3 \cdot (n - 1)\]

\[3 \cdot (n - 1) = 87,\ \ n - 1 = 29,\]

\[\ \ n = 30\]

\[S_{3} = \frac{a_{1} + a_{n}}{2} \cdot n = \frac{12 + 99}{2} \cdot\]

\[\cdot 30 = 111 \cdot 15 = 1665\]

\[Числа,\ кратные\ 5:\]

\[a_{n} = a_{1} + d(n - 1),\ \ \]

\[95 = 10 + 5 \cdot (n - 1)\]

\[5 \cdot (n - 1) = 85,\ \ n - 1 = 17,\]

\[\ \ n = 18\]

\[S_{5} = \frac{a_{1} + a_{n}}{2} \cdot n = \frac{10 + 95}{2} \cdot\]

\[\cdot 18 = 105 \cdot 9 = 945\]

\[Числа,\ кратные\ 15:\]

\[a_{n} = a_{1} + d(n - 1),\]

\[\ \ 90 = 15 + 15 \cdot (n - 1),\]

\[\ \ 15 \cdot (n - 1) = 75\]

\[n - 1 = 5,\ \ n = 6\]

\[S_{15} = \frac{a_{1} + a_{n}}{2} \cdot n = \frac{15 + 90}{2} \cdot\]

\[\cdot 6 = 105 \cdot 3 = 315\]

\[Тогда\ \ \ S = S_{0} - S_{3} - S_{5} +\]

\[+ S_{15} = 4905 - 1665 - 945 +\]

\[+ 315 = 2610.\]

\[Ответ:2610.\]