Решебник по алгебре 8 класс Мерзляк Проверь себя 2

\[\boxed{\text{Задание}\text{\ 2.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\boxed{\mathbf{1.}}\]

\[\frac{12m^{4}}{n^{10}} \cdot \frac{n^{5}}{36m^{8}} = \frac{12m^{4}n^{5}}{36m^{8}n^{10}} =\]

\[= \frac{1}{3m^{4}n^{5}}\]

\[Ответ:Б).\]

\[\boxed{\mathbf{2.}}\]

\[Ответ:Г).\]

\[\boxed{\mathbf{3.}}\]

\[Ответ:Б).\]

\[\boxed{\mathbf{4.}}\]

\[\frac{5a^{6}}{b^{8}}\ :\left( 10a^{3}b^{2} \right) = \frac{5a^{6}}{10a^{3}b^{2}b^{8}} =\]

\[= \frac{a^{3}}{2b^{10\ }}\]

\[Ответ:Г).\]

\[\boxed{\mathbf{5.}}\]

\[Ответ:А).\]

\[\boxed{\mathbf{6.}}\]

\[\frac{n^{3} - 3n}{64n^{2} - 1}\ \ :\frac{n^{4} - 27n}{64n^{2} + 16n + 1} =\]

\[= \frac{8n + 1}{(8n - 1)(n^{2} + 3n + 9)}\]

\[Ответ:А).\]

\[\boxed{\mathbf{7.}}\]

\[\left( - \frac{2a^{2}}{b^{3}} \right)^{4} = \frac{16a^{8}}{b^{12}}\]

\[Ответ:В).\]

\[\boxed{\mathbf{8.}}\]

\[\left( \frac{1}{a - 6} - \frac{1}{a + 6} \right)\ :\frac{2}{a + 6} =\]

\[= \frac{12}{(a - 6)(a + 6)}\ :\frac{2}{a + 6} =\]

\[= \frac{6}{a - 6}\]

\[Ответ:Б).\]

\[\boxed{\mathbf{9.}}\]

\[Ответ:В).\]

\[\boxed{\mathbf{10.}}\]

\[\frac{a^{2} - 4ab}{b^{2}} = \frac{a(a - 4b)}{b^{2}}\]

\[3a - 5b = 0,2 \cdot (2a + b)\]

\[3a - 5b = 0,4a + 0,2b\]

\[3a - 0,4a = 0,2b + 5b\]

\[2,6a = 5,2b\]

\[a = \frac{5,2b}{2,6}\]

\[a = 2b\]

\[Подставим\ в\ выражение:\ \]

\[\frac{2b(2b - 4b)}{b^{2}} = - \frac{4b^{2}}{b^{2}} = - 4\]

\[Ответ:Б).\]

\[\boxed{\mathbf{11.}}\]

\[x + \frac{1}{x} = 6;\ \ \ \ x^{2} + \frac{1}{x^{2}} = ?\]

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

\[= 2 + \left( x^{2} + \frac{1}{x^{2}} \right) = 6^{2}\]

\[x^{2} + \frac{1}{x^{2}} = 36 - 2 = 34\]

\[Ответ:В).\]

\[\boxed{\mathbf{12.}}\]

\[\frac{\frac{1}{a} + \frac{a}{b^{2}}}{\frac{a}{b^{2}} - \frac{1}{a}} = \frac{\frac{b^{2} + a^{2}}{ab^{2}}}{\frac{a^{2} - b^{2}}{ab^{2}}} =\]

\[Ответ:А).\]