Question

[IAm Fen Nấm]

So sánh

Căn 2006 - căn 2005 và căn 2007 - căn 2006 

Answer 1

[Capheny Bản Quyền]

\(\sqrt{2006}-\sqrt{2005}=\frac{\left(\sqrt{2006}-\sqrt{2005}\right)\left(\sqrt{2006}+\sqrt{2005}\right)}{\sqrt{2006}+\sqrt{2005}}=\frac{1}{\sqrt{2006}+\sqrt{2005}}\)   

\(\sqrt{2007}-\sqrt{2006}=\frac{\left(\sqrt{2007}-\sqrt{2006}\right)\left(\sqrt{2007}+\sqrt{2006}\right)}{\sqrt{2007}+\sqrt{2006}}=\frac{1}{\sqrt{2007}+\sqrt{2006}}\)   

Vì \(\sqrt{2006}+\sqrt{2005}< \sqrt{2007}+\sqrt{2006}\)   

Nên \(\frac{1}{\sqrt{2006}+\sqrt{2005}}>\frac{1}{\sqrt{2007}+\sqrt{2006}}\)   

Vậy \(\sqrt{2006}-\sqrt{2005}>\sqrt{2007}-\sqrt{2006}\)