答：
1
x^2+y^2-2x-6y+10=0,
(x^2-2x+1)+(y^2-6y+9)=0,
(x-1)^2+(y-3)^2=0,
x=1,y=3
2
9m^2-4n^2+4n-1
=9m^2-(4n^2-4n+1)
=9m^2-(2n-1)^2
=(3m+2n-1)(3m-2n+1)
3
(y+1)(y^2+1)-(y+1)^2
=(y+1)(y^2+1-y-1)
=(y+1)(y^2-y)
=(y-1)y(y+1)
4
a^2+b^2-6a+4b+13=0,
(a^2-6a+9)+(b^2+4b+4)=0,
(a-3)^2+(b+2)^2=0,
a=3,b=-2