已知m2-5m-1=0,则2m2−5m+1/m2=_.

问题描述:

已知m2-5m-1=0,则2m2−5m+

1
m2
=______.

∵m2-5m-1=0,
两边同时除以m得,m-

1
m
=5,
两边平方,得:
m2-2m•
1
m
+
1
m2
=25,
∴m2+
1
m2
=27,
∵2m2-5m+
1
m2
=m2-5m+m2+
1
m2

=1+27,
=28.