(a/b)≠√2,不妨设
（a/b）<√2
(a+2b)/(a+b)=1+[b/a+b]=1+[1/(a/b)+1]＞1+[1/(1+√2)]
=1+√2-1=√2
所以√2＜(a+2b)/(a+b)得证