题目条件不全哈 应该是sinB=√10/10吧
cos2A=2cosA^2-1=3/5
A、B为锐角,cosA>0,sinA>0,cosB>0
则:cosA=2/√5,sinA=1/√5
sinB=√10/10,则：cosB=3/√10
sinC=sin(π-A-B)=sin(A+B)
=sinAcosB+cosAsinB
=(1/√5) * (3/√10) + (2/√5) * (10/√10)
=1/√2
由正弦定理
a/sinA =b/sinB =c/sinC
代入条件得
√5*a = √10*b =√2*c
又a-b=√2 - 1
则：a=√2 ,b=1,c=√5