So sánh $\left(\dfrac{1}{45}\right)^{\dfrac{1}{45}}$ và $\left(\dfrac{1}{47}\right)^{\dfrac{1}{47}}$ 19/07/2021 Bởi Alice 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: \(\begin{array}{l}\text{Ta có:}\\\quad 45 < 47\qquad\qquad\ \ \ (1)\\\Leftrightarrow \dfrac{1}{45} > \dfrac{1}{47}\\\Leftrightarrow – \dfrac{1}{45} < – \dfrac{1}{47}\qquad (2)\\\text{Từ}\ (1)(2) \Rightarrow 45^{\displaystyle{-\dfrac{1}{45}}} < 47^{\displaystyle{-\dfrac{1}{47}}}\\\Leftrightarrow \left(45^{-1}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(47^{-1}\right)^{\displaystyle{\dfrac{1}{47}}}\\\Leftrightarrow \left(\dfrac{1}{45}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(\dfrac{1}{47}\right)^{\displaystyle{\dfrac{1}{47}}} \end{array}\) Bình luận
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:
\(\begin{array}{l}\text{Ta có:}\\
\quad 45 < 47\qquad\qquad\ \ \ (1)\\
\Leftrightarrow \dfrac{1}{45} > \dfrac{1}{47}\\
\Leftrightarrow – \dfrac{1}{45} < – \dfrac{1}{47}\qquad (2)\\
\text{Từ}\ (1)(2) \Rightarrow 45^{\displaystyle{-\dfrac{1}{45}}} < 47^{\displaystyle{-\dfrac{1}{47}}}\\
\Leftrightarrow \left(45^{-1}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(47^{-1}\right)^{\displaystyle{\dfrac{1}{47}}}\\
\Leftrightarrow \left(\dfrac{1}{45}\right)^{\displaystyle{\dfrac{1}{45}}} < \left(\dfrac{1}{47}\right)^{\displaystyle{\dfrac{1}{47}}}
\end{array}\)
`1/(45)>1/(47)`
`⇒a^(1/(45))<b^(1/(45)) `với` a>b`
`⇒(1/(45))^(1/(45))<(1/(47))^(1/(45)`