Question

已知：m²-3m+1=0，则m²+

1

m2

=______．

Answer 1

∵m²-3m+1=0，
∴m-3+

1

m

=0，即m+

1

m

=3，
∴m²+

1

m2

=（m+

1

m

）²-2=3²-2=7．
故答案为7．