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+
的值;1 x
(2)x2+
的值;1 x2
(3)x4+
的值. 1 x4
答
∵x2-4x+1=0,
∴x2+1=4x.
(1)x+
=1 x
=
x2+1 x
=4;4x x
(2)x2+
=(x+1 x2
)2-2=42-2=14;1 x
(3)x4+
=(x2+1 x4
)2-2=142-2=194.1 x2