Question

a) Không dùng máy tính để so sánh: \(\sqrt{2016}-\sqrt{2015}\) và \(\sqrt{2017}-\sqrt{2016}\)

Answer 1

\(\sqrt{2016}-\sqrt{2015}=\frac{\sqrt{2016}+\sqrt{2015}}{\left(\sqrt{2016}-\sqrt{2015}\right)\left(\sqrt{2016}+\sqrt{2015}\right)}=\frac{1}{\sqrt{2016}+\sqrt{2015}}\)

Tương tự \(\sqrt{2017}-\sqrt{2016}=\frac{1}{\sqrt{2017}+\sqrt{2016}}\)

Mà \(\sqrt{2017}+\sqrt{2016}>\sqrt{2016}+\sqrt{2015}\Rightarrow\frac{1}{\sqrt{2016}+\sqrt{2015}}>\frac{1}{\sqrt{2017}+\sqrt{2016}}\)

\(\Rightarrow\sqrt{2016}-\sqrt{2015}>\sqrt{2017}-\sqrt{2016}\)