已知a+1a=3,求:(1)a2+1a2的值.(2)a4+1a4的值.-数学

题目简介

已知a+1a=3,求:(1)a2+1a2的值.(2)a4+1a4的值.-数学

题目详情

已知a+
1
a
=3
,求:
(1)a2+
1
a2
的值.
(2)a4+
1
a4
的值.
题型:解答题难度:中档来源:不详

答案

(1)∵a2+class="stub"1
a2
=(a+class="stub"1
a
)2-2,
又∵a+class="stub"1
a
=3,
a2+class="stub"1
a2
=32-2=7;

(2)a4+class="stub"1
a4
=(a2+class="stub"1
a2
)2-2
=72-2
=47.

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