> 数学 >
已知a+
1
a
=
10
,求a2+
1
a2
a2-
1
a2
的值.
人气:272 ℃ 时间:2020-06-27 12:22:51
解答
a+
1
a
=
10

∴a2+
1
a2
=(a+
1
a
2-2=10-2=8,
∴(a-
1
a
2=(a+
1
a
2-4=10-4=6,
∴a-
1
a
6

∴a2-
1
a2
=(a+
1
a
)(a-
1
a
)=
10
×(±
6
)=±2
15
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