∵实数m满足：m²-5m-1=0，
∴m²=5m+1，
∴3m2−10m+

1

m2

=3（5m+1）-10m+

1

m2

=5m+3+

1

m2

=

(5m+3)(5m+1)+1

m2

=

25m2+4(5m+1)

m2

=

25m2+4m2

m2

=29．
故答案是：29．