Trong các khẳng định sau, khẳng định nào sai? ((1 - (căn 2 / 2))^2018 < ((1 - (căn 2 / 2))^2017

* Hướng dẫn giải

Đáp án D

Ta có

$$\begin{gathered} +\left\{\begin{array}{l}0<1-\frac{\sqrt{2}}{2}<1\\ 2018>2017\end{array}\right. \\ \Rightarrow {\left(1-\frac{\sqrt{2}}{2}\right)}^{2018}<{\left(1-\frac{\sqrt{2}}{2}\right)}^{2017} \end{gathered}$$  

$$\begin{gathered} +\left\{\begin{array}{l}2>1\\ \sqrt{2}+1>\sqrt{3}\end{array}\right. \\ \Rightarrow 2^{\sqrt{2}+1}>2^{\sqrt{3}} \end{gathered}$$.

$$\begin{gathered} +\left\{\begin{array}{l}0<\sqrt{2}-1<1\\ 2017<2018\end{array}\right. \\ \Rightarrow {\left(\sqrt{2}-1\right)}^{2017}>{\left(\sqrt{2}-1\right)}^{2018} \end{gathered}$$     

$+\left\{\begin{array}{l}0<\sqrt{3}-1<1\\ 2018>2017\end{array}\right.\Rightarrow {\left(\sqrt{3}-1\right)}^{2018}<{\left(\sqrt{3}-1\right)}^{2017}$