Ta có `\sqrt{2010} - \sqrt{2009}`
` = ((\sqrt{2010} - \sqrt{2009})(\sqrt{2010} + \sqrt{2009}))/(\sqrt{2010} + \sqrt{2009})`
`= (2010 - 2009)/(\sqrt{2010} + \sqrt{2009})`
` = 1/(\sqrt{2010} + \sqrt{2009})`
Lại có :
`\sqrt{2009} - \sqrt{2008}`
` = ((\sqrt{2009} - \sqrt{2008})(\sqrt{2009} + \sqrt{2008}))/(\sqrt{2009} + \sqrt{2008})`
`= (2009 - 2008)/(\sqrt{2009} + \sqrt{2008})`
` = 1/(\sqrt{2009} + \sqrt{2008})`
Ta thấy :
`\sqrt{2010} + \sqrt{2009} > \sqrt{2009} + \sqrt{2008}`
`=> 1/(\sqrt{2010} + \sqrt{2009}) < 1/(\sqrt{2009} + \sqrt{2008})`
`=> \sqrt{2010} - \sqrt{2009} < \sqrt{2009} - \sqrt{2008}`
