Решебник по алгебре 7 класс Мерзляк ФГОС Задание 549

 

\[\boxed{\text{549\ (549).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ 16 - (6 - 11x)^{2} = 0\]

\[(4 - 6 + 11x)(4 + 6 - 11x) = 0\]

\[(11x - 2)(10 - 11x) = 0\]

\[11x - 2 = 0;\ \ \ \ \ \ \ \ \ 10 - 11x = 0\]

\[11x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - 11x = - 10\]

\[x = \frac{2}{11}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{10}{11}\]

\[Ответ:x = \frac{2}{11};\ \frac{10}{11}.\]

\[( - 2m - 32)(16m + 6) = 0\]

\[Ответ:\ x = - 16;\ - \frac{3}{8}.\]

\[\boxed{\text{549.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ y^{2} - 6y = 0\]

\[y \cdot (y - 6) = 0\]

\[y = 0\ \ или\ \ y - 6 = 0\]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }y = 6\]

\[Ответ:y = 0;6.\]

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

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

\[x = 0\ \ или\ \ x + 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 1\]

\[Ответ:x = 0;\ - 1.\]

\[3)\ 4m^{2} - 20m = 0\]

\[4m \cdot (m - 5) = 0\]

\[4m = 0\ \ или\ \ m - 5 = 0\]

\[\ \ \ m = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m = 5\]

\[Ответ:m = 0;\ 5.\]

\[4)\ 13x^{2} + x = 0\]

\[x \cdot (13x + 1) = 0\]

\[x = 0\ \ или\ \ 13x + 1 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{1}{13}\]

\[Ответ:x = 0;\ - \frac{1}{13}.\]

\[5)\ 9x^{2} - 6x = 0\]

\[3x \cdot (3x - 2) = 0\]

\[3x = 0\ \ или\ \ 3x - 2 = 0\]

\[\ \ \ x = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{2}{3}.\]

\[Ответ:x = 0;\frac{2}{3}.\]

\[6)\ 12x - 0,3x^{2} = 0\]

\[0,3x \cdot (40 - x) = 0\]

\[x = 0\ \ или\ 40 - x = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 40.\]

\[Ответ:x = 0;40.\ \]