Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 564

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\[1)\ \left( \frac{10}{11} \right)^{2,3}\text{\ \ }и\ \ \left( \frac{12}{11} \right)^{2,3};\]

\[\frac{10}{11} < \frac{12}{11};\]

\[\left( \frac{10}{11} \right)^{2,3} < \left( \frac{12}{11} \right)^{2,3}.\]

\[2)\ {2,5}^{- 8,1}\text{\ \ }и\ \ {2,6}^{- 8,1};\]

\[\left( \frac{10}{25} \right)^{8,1} > \left( \frac{10}{26} \right)^{8,1}\]

\[\frac{10}{25} > \frac{10}{26}\]

\[{2,5}^{- 8,1} > {2,6}^{- 8,1}.\]

\[3)\ \left( \frac{14}{15} \right)^{\frac{3}{4}}\text{\ \ }и\ \ \left( \frac{15}{16} \right)^{\frac{3}{4}};\]

\[\frac{14}{15} = \frac{224}{240}\text{\ \ }и\ \ \frac{15}{16} = \frac{225}{240};\]

\[\frac{224}{240} < \frac{225}{240};\]

\[\frac{14}{15} < \frac{15}{16};\]

\[\left( \frac{14}{15} \right)^{- 6} < \left( \frac{15}{16} \right)^{- 6}.\]

\[4)\ \left( 2\sqrt[3]{5} \right)^{- 0.2}\text{\ \ }и\ \ \left( 5\sqrt[3]{2} \right)^{- 0.2};\]

\[\left( 2\sqrt[3]{5} \right)^{3} = 8 \bullet 5 = 40;\text{\ \ }\left( \sqrt[3]{2} \right)^{3} =\]

\[= 125 \bullet 2 = 250;\]

\[40 < 250;\]

\[2\sqrt[3]{5} < 5\sqrt[3]{2};\]

\[\left( 2\sqrt{5} \right)^{- 0,2} > \left( 5\sqrt[3]{2} \right)^{- 0,2}.\]