已知x/x2−x+1=1/3,求x2x4+x2+1的值.

问题描述:

已知

x
x2−x+1
=
1
3
,求
x2
x4+x2+1
的值.

x
x2−x+1
=
1
3

∴x2=4x-1,
∴原式=
4x−1
(4x−1)2+4x

=
4x−1
16x2−8x+1+4x

=
4x−1
16x2−4x+1

=
4x−1
16(4x−1)−4x+1

=
4x−1
15(4x−1)

=
1
15