Question

Không dùng máy tính so sánh \(\sqrt{2019}-\sqrt{2018}\) và\(\sqrt{2018}-\sqrt{2017}\)

Answer 1

Lời giải:

\(\sqrt{2019}-\sqrt{2018}=\frac{2019-2018}{\sqrt{2019}+\sqrt{2018}}=\frac{1}{\sqrt{2019}+\sqrt{2018}}\)

\(\sqrt{2018}-\sqrt{2017}=\frac{2018-2017}{\sqrt{2018}+\sqrt{2017}}=\frac{1}{\sqrt{2018}+\sqrt{2017}}\)

Dễ thấy \(\sqrt{2019}+\sqrt{2018}>\sqrt{2018}+\sqrt{2017}\Rightarrow \frac{1}{\sqrt{2019}+\sqrt{2018}}< \frac{1}{\sqrt{2018}+\sqrt{2017}}\)

\(\Rightarrow \sqrt{2019}-\sqrt{2018}< \sqrt{2018}-\sqrt{2017}\)