Question

So sánh \(\sqrt{2013}-\sqrt{2011}\) và \(\sqrt{2012}-\sqrt{2010}\)

Giúp mình gấp

Answer 1

+ \(\sqrt{2013}-\sqrt{2011}=\frac{\left(\sqrt{2013}-\sqrt{2011}\right)\left(\sqrt{2013}+\sqrt{2011}\right)}{\sqrt{2013}+\sqrt{2011}}\)

\(=\frac{2}{\sqrt{2013}+\sqrt{2011}}\)

+ \(\sqrt{2012}-\sqrt{2010}=\frac{\left(\sqrt{2012}-\sqrt{2010}\right)\left(\sqrt{2012}+\sqrt{2010}\right)}{\sqrt{2012}+\sqrt{2010}}\)

\(=\frac{2}{\sqrt{2012}+\sqrt{2010}}\)

+ \(\sqrt{2013}+\sqrt{2011}>\sqrt{2012}+\sqrt{2010}\)

\(\Rightarrow\frac{2}{\sqrt{2013}+\sqrt{2011}}< \frac{2}{\sqrt{2012}+\sqrt{2010}}\)

\(\Rightarrow\sqrt{2013}-\sqrt{2011}< \sqrt{2012}-\sqrt{2010}\)