Ta có: \(\sqrt{2018}-\sqrt{2019}\)
\(=\frac{\left(\sqrt{2018}-\sqrt{2019}\right)\left(\sqrt{2018}+\sqrt{2019}\right)}{\sqrt{2018}+\sqrt{2019}}\)
\(=\frac{2018-2019}{\sqrt{2018}+\sqrt{2019}}=\frac{-1}{\sqrt{2018}+\sqrt{2019}}\)
Ta có: \(\sqrt{2019}-\sqrt{2020}\)
\(=\frac{\left(\sqrt{2019}-\sqrt{2020}\right)\left(\sqrt{2019}+\sqrt{2020}\right)}{\sqrt{2019}+\sqrt{2020}}\)
\(=\frac{-1}{\sqrt{2019}+\sqrt{2020}}\)
Ta có: \(\sqrt{2018}+\sqrt{2019}< \sqrt{2019}+\sqrt{2020}\)
\(\Leftrightarrow\frac{1}{\sqrt{2018}+\sqrt{2019}}>\frac{1}{\sqrt{2019}+\sqrt{2020}}\)
\(\Leftrightarrow\frac{-1}{\sqrt{2018}+\sqrt{2019}}< \frac{-1}{\sqrt{2019}+\sqrt{2020}}\)
hay \(\sqrt{2018}-\sqrt{2019}< \sqrt{2019}-\sqrt{2020}\)