如果x满足x2-3x+1=0,那么代数式x2+1/x2=_.

问题描述:

如果x满足x2-3x+1=0,那么代数式x2+

1
x2
=______.

∵x2-3x+1=0,
∴x-3+

1
x
=0,即x+
1
x
=3,
∴x2+
1
x2
=(x+
1
x
2-2=32-2=7.
故答案为7.