Question

so sánh: \(\sqrt{14}-\sqrt{13}\) và \(2\sqrt{3}-\sqrt{11}\)

Answer 1

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

\(2\sqrt{3}-\sqrt{11}=\sqrt{12}-\sqrt{11}=\frac{1}{\sqrt{12}+\sqrt{11}}\)

Mà \(\sqrt{14}+\sqrt{13}>\sqrt{12}+\sqrt{11}>0\)

\(\Rightarrow\frac{1}{\sqrt{14}+\sqrt{13}}< \frac{1}{\sqrt{12}+\sqrt{11}}\)

\(\Rightarrow\sqrt{14}-\sqrt{13}< 2\sqrt{3}-\sqrt{11}\)