Question

So sánh :\(\sqrt{2009}-\sqrt{2008};\sqrt{2008}-\sqrt{2007}\) 

Answer 1

\(\sqrt{2009}-\sqrt{2008}

Answer 2

\(\frac{1}{\sqrt{2009}-\sqrt{2008}}=\frac{\sqrt{2009}+\sqrt{2008}}{\left(\sqrt{2009}+\sqrt{2008}\right)\left(\sqrt{2009}-\sqrt{2008}\right)}=\frac{\sqrt{2009}+\sqrt{2008}}{2009-2008}=\sqrt{2009}+\sqrt{2008}\)

CMTT : \(\frac{1}{\sqrt{2008}-\sqrt{2007}}=\sqrt{2008}+\sqrt{2007}\)

Vì \(\sqrt{2009}+\sqrt{2008}>\sqrt{2008}+\sqrt{2007}\)

=> \(\frac{1}{\sqrt{2009}-\sqrt{2008}}\sqrt{2008}-\sqrt{2007}\)