已知x/x2−x+1=1/3,求x2x4+x2+1的值.
问题描述:
已知
=x
x2−x+1
,求1 3
的值. x2
x4+x2+1
答
∵
=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