∵a＞b＞0∴a²+b²-6ab=0等式两边同除以b²，得：∴（a/b)²+1-6（a/b)=0记t=a/b【t＞1】,则上式可化为：t²-6t+1=0△=36-4=32∴t=（6+4√2）/2=3+2√2,即：a/b=3+2√2∴（a+b）/(a-b)=(a/b+1)/(a/b-1)=(3+2√2+1)/(3+2√2-1)=(4+2√2)/(2+2√2)=(2+√2）/(1+√2)=√2
