Question

so sánh a=\(\sqrt{15}-\sqrt{14}\) và b=\(\sqrt{14}-\sqrt{13}\)

Answer 1

ta có:

+) \(\left(\sqrt{15}-\sqrt{14}\right)\left(\sqrt{15}+\sqrt{14}\right)=1\)

\(\Rightarrow\sqrt{15}-\sqrt{14}=\frac{1}{\sqrt{15}+\sqrt{14}}\)

+) \(\left(\sqrt{14}-\sqrt{13}\right)\left(\sqrt{14}+\sqrt{13}\right)=1\)

\(\Rightarrow\sqrt{14}-\sqrt{13}=\frac{1}{\sqrt{14}+\sqrt{13}}\)

vì \(\sqrt{15}+\sqrt{14}>\sqrt{14}+\sqrt{13}\) nên \(\frac{1}{\sqrt{15}+\sqrt{14}}< \frac{1}{\sqrt{14}+\sqrt{13}}\)

\(\Rightarrow\sqrt{15}-\sqrt{14}< \sqrt{14}-\sqrt{13}\)