ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 484

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\[1)\ 5^{\sqrt{71}}\ или\ 5^{\sqrt{69}};\]

\[71 > 69;\]

\[\sqrt{71} > \sqrt{69};\]

\[5^{\sqrt{71}} > 5^{\sqrt{69}};\]

\[Ответ:\ \ 5^{\sqrt{71}}.\]

\[2)\ \left( \frac{1}{2} \right)^{\sqrt{3}}\ или\ \left( \frac{1}{2} \right)^{\sqrt{2}};\]

\[3 > 2;\]

\[\sqrt{3} > \sqrt{2};\]

\[\left( \frac{1}{2} \right)^{\sqrt{3}} < \left( \frac{1}{2} \right)^{\sqrt{2}};\]

\[Ответ:\ \ \left( \frac{1}{2} \right)^{\sqrt{2}}.\]

\[3)\ 3^{- \sqrt{3}}\ или\ 3^{- \sqrt{2}};\]

\[3 > 2;\]

\[\sqrt{3} > \sqrt{2};\]

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

\[3^{- \sqrt{3}} < 3^{- \sqrt{2}};\]

\[Ответ:\ \ 3^{- \sqrt{2}}.\]

\[4)\ 2^{\sqrt{3}}\ или\ 2^{1,7};\]

\[300 > 289;\]

\[\sqrt{300} > 17;\]

\[\sqrt{3} > 1,7;\]

\[2^{\sqrt{3}} > 2^{1,7};\]

\[Ответ:\ \ 2^{\sqrt{3}}.\]