Решебник по алгебре 7 класс Мерзляк ФГОС Задание 550

 

\[\boxed{\text{550\ (550).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ (7n + 4)^{2} - 9 =\]

\[= (7n + 4 - 3)(7n + 4 + 3) =\]

\[= (7n + 1)(7n + 7) =\]

\[= 7 \cdot (7n + 1)(n + 1) \Longrightarrow\]

\[\Longrightarrow делится\ на\ 7.\]

\[2)\ (8n + 1)^{2} - (3n - 1)^{2} =\]

\[= (5n + 2) \cdot 11 \cdot n \Longrightarrow делится\ \]

\[на\ 11.\]

\[3)\ (3n + 7)^{2} - (3n - 5)^{2} =\]

\[= 12 \cdot (6n + 2) =\]

\[= 12 \cdot 2 \cdot (3n + 1) =\]

\[= 24 \cdot (3n + 1) \Longrightarrow делится\ на\ \]

\[24.\]

\[4)\ (7n + 6)^{2} - (2n - 9)^{2} =\]

\[= (5n + 15)(9n - 3) =\]

\[= 5 \cdot (n + 3) \cdot 3 \cdot (3n - 1) =\]

\[= 15 \cdot (n + 3)(3n - 1) \Longrightarrow\]

\[\Longrightarrow делится\ на\ 15.\]

\[\boxed{\text{550.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ x^{2} - x = 0\]

\[x \cdot (x - 1) = 0\]

\[x = 0\ \ или\ \ x - 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 1.\]

\[Ответ:x = 0;1.\]

\[2)\ p^{2} + 15p = 0\]

\[p \cdot (p + 15) = 0\]

\[p = 0\ \ или\ \ p + 15 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ p = - 15.\]

\[Ответ:p = 0;\ - 15.\]

\[3)\ 5x^{2} - 30x = 0\]

\[5x \cdot (x - 6) = 0\]

\[x = 0\ \ или\ \ x - 6 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 6\]

\[Ответ:x = 0;6.\]

\[4)\ 14x^{2} + 18x = 0\]

\[2x \cdot (7x + 9) = 0\]

\[x = 0\ \ или\ \ 7x + 9 = 0\]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }x = - \frac{9}{7} =\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - 1\frac{2}{7}.\]

\[Ответ:\ x = 0;\ - 1\frac{2}{7}\text{.\ }\]