Решебник по алгебре 8 класс Мерзляк ФГОС Задание 872

 

\[\boxed{\mathbf{872\ (872).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 2^{- 3} + 4^{- 2} = 2^{- 3} + \left( 2^{2} \right)^{- 2} =\]

\[= 2^{- 3} + 2^{- 4} = 2^{- 4} \cdot (2 + 1) =\]

\[= \frac{3}{16}\]

\[2)\ \left( \frac{3}{5} \right)^{- 2} + ( - 1,8){^\circ} - 5^{- 1} =\]

\[= \frac{25}{9} + 1 - \frac{1}{5} = \frac{125 + 45 - 9}{45} =\]

\[= \frac{161}{45} = 3\frac{26}{45}\]

\[3)\ \left( \frac{1}{3} \right)^{- 3} \cdot \left( \frac{2}{3} \right)^{2} = \frac{3^{3} \cdot 2^{2}}{3^{2}} =\]

\[= 3 \cdot 4 = 12\]

\[4)\ 2^{- 3} - 6^{- 1} + 3^{- 2} =\]

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

\[= \frac{1}{8} - \frac{1}{6} + \frac{1}{9} = \frac{54 - 72 + 48}{432} =\]

\[= \frac{30}{432} = \frac{15}{216} = \frac{5}{72}\]

\[\boxed{\mathbf{8}\mathbf{72}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ b = - 1:\]

\[4(b + 1) = 4( - 1 + 1) = 0;\]

\[b - 2 = - 1 - 2 = - 3;\]

\[4(b + 1) > b - 2.\]

\[2)\ b = 0:\]

\[4(b + 1) = 4(0 + 1) = 4;\]

\[b - 2 = 0 - 2 = - 2;\]

\[4(b + 1) > b - 2.\]

\[3)\ b = 3:\]

\[4(b + 1) = 4(3 + 1) = 16;\]

\[b - 2 = 3 - 2 = 1;\]

\[4(b + 1) > (b - 2).\]

\[Проверим:\]

\[4(b + 1) - (b - 2) =\]

\[= 4b + 4 - b + 2 = 3b + 6\]

\[3b + 6 > 0\]

\[3b > - 6\]

\[b > - 2.\]

\[Нет,\ только\ при\ b > - 2.\]