若x2-4x+1=0,求: (1)x+1/x的值; (2)x2+1/x2的值; (3)x4+1/x4的值.

问题描述:

若x2-4x+1=0,求:
(1)x+

1
x
的值;
(2)x2+
1
x2
的值;
(3)x4+
1
x4
的值.

∵x2-4x+1=0,
∴x2+1=4x.
(1)x+

1
x
=
x2+1
x
=
4x
x
=4;
(2)x2+
1
x2
=(x+
1
x
2-2=42-2=14;
(3)x4+
1
x4
=(x2+
1
x2
2-2=142-2=194.