∵a²+b²-6ab=0
∴(a-b)²=4ab
(a+b)²=8ab
∵a>b>0
∴a-b>0,a+b>0
∴a-b=2√(ab),a+b=2√2√(ab)
∴(a+b)/(b-a)
=-(a+b)/(a-b)
=-2√(ab)/[2√2√(ab)]
=-1/√2
=-√2
∵a²+b²-6ab=0
∴(a-b)²=4ab
(a+b)²=8ab
∵a>b>0
∴a-b>0,a+b>0
∴a-b=2√(ab),a+b=2√2√(ab)
∴(a+b)/(b-a)
=-(a+b)/(a-b)
=-2√(ab)/[2√2√(ab)]
=-1/√2
=-√2