a2+b2-10a-6b+34=0即a2-10a+25+b2-6b+9=0即(a-5)2+(b-3)2=0因为(a-5)2,(b-3)2大于或等于0,所以a=5,b=3
所以(a+b)/(a-b)=(5+3)/(5-3)=8/2=4
(a2-10a+25)+(b2-6b+9)=0
(a-5)2=0 (b-3)2=0
a=5 b=3
∵a2+b2-10a-6b+34=0
∴a^2-10a+25+b^2-6b+9=0
∴(a-5)^2+(b-3)^2=0
∵(a-5)^2≥0,(b-3)^2≥0
∴a=5,b=3
∴(a+b)/(a-b)=(5+3)(5-3)=16