Theo đề ta có:
$\sqrt{2020}$ - $\sqrt{2021}$
= $\frac{(\sqrt{2020}- \sqrt{2021})×(\sqrt{2020}+ \sqrt{2021})}{\sqrt{2020}+ \sqrt{2021}}$
= $\frac{-1}{\sqrt{2020}+ \sqrt{2021}}$
Lại có:
$\sqrt{2019}$ - $\sqrt{2020}$
= $\frac{(\sqrt{2019}- \sqrt{2020})×(\sqrt{2019}+ \sqrt{2020})}{\sqrt{2019}+ \sqrt{2020}}$
=$\frac{-1}{\sqrt{2019}+ \sqrt{2020}}$
Mà $\sqrt{2019}$ - $\sqrt{2020}$ < $\sqrt{2020}$ - $\sqrt{2021}$
⇒ $\frac{1}{\sqrt{2019}+ \sqrt{2020}}$ > $\frac{1}{\sqrt{2020}+ \sqrt{2021}}$
⇒ $\frac{-1}{\sqrt{2019}+ \sqrt{2020}}$ < $\frac{-1}{\sqrt{2020}+ \sqrt{2021}}$
⇒ $\sqrt{2019}$ - $\sqrt{2020}$ < $\sqrt{2020}$ - $\sqrt{2021}$