Toán so sánh căn 2021- căn 2020 và căn 2022- căn 2021 11/07/2021 By Raelynn so sánh căn 2021- căn 2020 và căn 2022- căn 2021
Đáp án: $\sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021} $ Giải thích các bước giải: Ta có: $\begin{array}{l}\sqrt {2021} – \sqrt {2020} = \dfrac{{{{\left( {\sqrt {2021} } \right)}^2} – {{\left( {\sqrt {2020} } \right)}^2}}}{{\sqrt {2021} + \sqrt {2020} }} = \dfrac{1}{{\sqrt {2021} + \sqrt {2020} }}\\\sqrt {2022} – \sqrt {2021} = \dfrac{{{{\left( {\sqrt {2022} } \right)}^2} – {{\left( {\sqrt {2021} } \right)}^2}}}{{\sqrt {2022} + \sqrt {2021} }} = \dfrac{1}{{\sqrt {2022} + \sqrt {2021} }}\end{array}$ Mà $0 < \sqrt {2021} + \sqrt {2020} < \sqrt {2022} + \sqrt {2021} $ $\begin{array}{l} \Rightarrow \dfrac{1}{{\sqrt {2021} + \sqrt {2020} }} > \dfrac{1}{{\sqrt {2022} + \sqrt {2021} }}\\ \Rightarrow \sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021} \end{array}$ Vậy$\sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021} $ Trả lời
Đáp án:
$\sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021} $
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\sqrt {2021} – \sqrt {2020} = \dfrac{{{{\left( {\sqrt {2021} } \right)}^2} – {{\left( {\sqrt {2020} } \right)}^2}}}{{\sqrt {2021} + \sqrt {2020} }} = \dfrac{1}{{\sqrt {2021} + \sqrt {2020} }}\\
\sqrt {2022} – \sqrt {2021} = \dfrac{{{{\left( {\sqrt {2022} } \right)}^2} – {{\left( {\sqrt {2021} } \right)}^2}}}{{\sqrt {2022} + \sqrt {2021} }} = \dfrac{1}{{\sqrt {2022} + \sqrt {2021} }}
\end{array}$
Mà $0 < \sqrt {2021} + \sqrt {2020} < \sqrt {2022} + \sqrt {2021} $
$\begin{array}{l}
\Rightarrow \dfrac{1}{{\sqrt {2021} + \sqrt {2020} }} > \dfrac{1}{{\sqrt {2022} + \sqrt {2021} }}\\
\Rightarrow \sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021}
\end{array}$
Vậy$\sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021} $