a^2+b^2+2a+8b=-17
a^2+b^2+2a+8b+17=0
a^2+2a+1+b^2+8b+16=0
（a+1）^2+（b+4）^2=0
a+1=0,b+4=0
a=-1,b=-4
根号a/b+根号b/a=1/2+2=5/2