Question

 

So sánh

Answer 1

Ta có: \(\left\{{}\begin{matrix}\sqrt{2008}+\sqrt{2005}< \sqrt{2015}+\sqrt{2009}\\\sqrt{2010}+\sqrt{2007}< \sqrt{2015}+\sqrt{2009}\end{matrix}\right.\)

\(\Rightarrow\dfrac{1}{\sqrt{2008}+\sqrt{2005}}+\dfrac{1}{\sqrt{2010}+\sqrt{2007}}>\dfrac{2}{\sqrt{2015}+\sqrt{2009}}\)

\(\Leftrightarrow\dfrac{\sqrt{2008}-\sqrt{2005}}{3}+\dfrac{\sqrt{2010}-\sqrt{2007}}{3}>\dfrac{\sqrt{2015}-\sqrt{2009}}{3}\)

\(\Leftrightarrow\sqrt{2008}+\sqrt{2009}+\sqrt{2010}>\sqrt{2005}+\sqrt{2007}+\sqrt{2015}\)