a=根号下2008—根号下2009 ,b=根号下2009-根号下2010,比较a b大小

问题描述:

a=根号下2008—根号下2009 ,b=根号下2009-根号下2010,比较a b大小

a-b
=√2008-√2009-(√2009-√2010)
=√2008-√2009-√2009+√2010
=√2008+√2010>0
所以a-b>0
即a>b

b-a=2√2009-√2008-√2010
(2√2009)^2-(√2008+√2010)^2 =2*2009-2√2008*2010>0
b-a>0
b>a