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Câu hỏi: Khẳng định nào sau đây đúng?
A. ${{\left( \sqrt{5}+2 \right)}^{-2017}}<{{\left( \sqrt{5}+2 \right)}^{-2018}}$
B. ${{\left( \sqrt{5}+2 \right)}^{2018}}>{{\left( \sqrt{5}+2 \right)}^{2019}}$
C. ${{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}$
D. ${{\left( \sqrt{5}-2 \right)}^{2018}}<{{\left( \sqrt{5}-2 \right)}^{2019}}$
A. ${{\left( \sqrt{5}+2 \right)}^{-2017}}<{{\left( \sqrt{5}+2 \right)}^{-2018}}$
B. ${{\left( \sqrt{5}+2 \right)}^{2018}}>{{\left( \sqrt{5}+2 \right)}^{2019}}$
C. ${{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}$
D. ${{\left( \sqrt{5}-2 \right)}^{2018}}<{{\left( \sqrt{5}-2 \right)}^{2019}}$
$\left\{ \begin{aligned}
& 0<\sqrt{5}-2<1 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}\Rightarrow $ Đáp án C đúng.
$\left\{ \begin{aligned}
& \sqrt{5}+2>1 \\
& -2017>-2018 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}+2 \right)}^{-2017}}>{{\left( \sqrt{5}+2 \right)}^{-2018}}\Rightarrow $ Đáp án A sai.
$\left\{ \begin{aligned}
& \sqrt{5}+2 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}+2 \right)}^{2018}}<{{\left( \sqrt{5}+2 \right)}^{2019}}\Rightarrow $ Đáp án B sai.
$\left\{ \begin{aligned}
& 0<\sqrt{5}-2<1 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}\Rightarrow $ Đáp án D sai.
& 0<\sqrt{5}-2<1 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}\Rightarrow $ Đáp án C đúng.
$\left\{ \begin{aligned}
& \sqrt{5}+2>1 \\
& -2017>-2018 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}+2 \right)}^{-2017}}>{{\left( \sqrt{5}+2 \right)}^{-2018}}\Rightarrow $ Đáp án A sai.
$\left\{ \begin{aligned}
& \sqrt{5}+2 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}+2 \right)}^{2018}}<{{\left( \sqrt{5}+2 \right)}^{2019}}\Rightarrow $ Đáp án B sai.
$\left\{ \begin{aligned}
& 0<\sqrt{5}-2<1 \\
& 2018<2019 \\
\end{aligned} \right.\Rightarrow {{\left( \sqrt{5}-2 \right)}^{2018}}>{{\left( \sqrt{5}-2 \right)}^{2019}}\Rightarrow $ Đáp án D sai.
Đáp án C.