> 数学 >
x
x2+x+1
=a,a≠0,求
x2
x4+x2+1
的值.
人气:289 ℃ 时间:2020-03-29 14:55:25
解答
x
x2+x+1
=a(a≠0),x≠0,
x2+x+1
x
=
1
a
,即x+
1
x
=
1
a
-1,
两边平方得:(x+
1
x
2=(
1−a
a
2,即x2+
1
x2
+2=
(1−a)2
a2

整理得:x2+
1
x2
=
a2−2a+1
a2

∴原式=
1
x2+
1
x2
+1
=
1
−2a+1
a2
=
a2
1−2a
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