问题 填空题
已知
x
x2-x+1
=7
,求
x2
x4+x2+1
的值.
答案

x2-x+1
x
=
1
7

x+

1
x
-1=
1
7

x+

1
x
=
8
7
(3分)

又∵x2+

1
x2
=(x+
1
x
)2-2=
64
49
-2=-
34
49
(6分)

x2
x4+x2+1
=
1
x2+
1
x2
+1
=
1
-
34
49
+1
=
49
15
(10分)

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