问题 解答题
已知x2-4x+1=0,求x4+
1
x4
的值.______
答案

∵x2-4x+1=0,

∴x-4+

1
x
=0,

即x+

1
x
=4,

∴x2+

1
x2
=(x+
1
x
2-2,

=42-2,

=14,

∴x4+

1
x4
=(x2+
1
x2
2-2,

=142-2,

=194.

故答案为:194.

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