问题 解答题
已知a+
1
a
=3
,求
(1)a2+
1
a2
的值;
(2)a3-a2-5a+2010的值.
答案

(1)∵a+

1
a
=3,

a2+

1
a2
=(a+
1
a
2-2=32-2=7

(2)a3-a2-5a+2010

=a3+a-a2-6a+2010

=a2(a+

1
a
)-a2-6a+2010

=3a2-a2-6a+2010

=2a2-6a+2010

=2a2+2-6a+2008

=2a(a+

1
a
)-6a+2008

=6a-6a+2008

=2008

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