∵a=(2,1),a+b=5根号2∴a=根号2^2+1^2=根号5 （a+b)^2=50即（a+b)^2=a^2+b^2+2ab=5+b^2+20=25+b^2=50∴b=±5
|a+b|^2=a^2+2ab+b^250=5+2*10+b^2b^2=25|b|=5
