∵ m²+n²=6n-4m-13
∴ m²+4m+n²-6n+13=0
(m²+4m+4)+(n²-6n+9)=0
(m+2)²+(n-3)²=0
∴ m+2=0 且n-3=0
m=-2,n=3
∴ m²-n²=(-2)²-3²
=4-9
= -5