## so sánh căn 2021- căn 2020 và căn 2022- căn 2021

Question

so sánh căn 2021- căn 2020 và căn 2022- căn 2021

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9 months 2020-10-31T09:00:40+00:00 1 Answers 155 views 1

## Answers ( )

1. 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$\sqrt {2021} – \sqrt {2020} > \sqrt {2022} – \sqrt {2021}$