So sánh $\left(\dfrac{1}{45}\right)^{\dfrac{1}{45}}$ và $\left(\dfrac{1}{47}\right)^{\dfrac{1}{47}}$

Đáp án:

\(\left(\dfrac{1}{45}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(\dfrac{1}{47}\right)^{\displaystyle{\dfrac{1}{47}}} \) 

Giải thích các bước giải:

\(\begin{array}{l}\text{Ta có:}\\
\quad 45 < 47\qquad\qquad\ \ \ (1)\\
\Leftrightarrow \dfrac{1}{45} > \dfrac{1}{47}\\
\Leftrightarrow – \dfrac{1}{45} < – \dfrac{1}{47}\qquad (2)\\
\text{Từ}\ (1)(2) \Rightarrow 45^{\displaystyle{-\dfrac{1}{45}}} < 47^{\displaystyle{-\dfrac{1}{47}}}\\
\Leftrightarrow \left(45^{-1}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(47^{-1}\right)^{\displaystyle{\dfrac{1}{47}}}\\
\Leftrightarrow \left(\dfrac{1}{45}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(\dfrac{1}{47}\right)^{\displaystyle{\dfrac{1}{47}}} 
\end{array}\)