已知a2-3a+1=0,则a4+1a4=______.-数学

题目简介

已知a2-3a+1=0,则a4+1a4=______.-数学

题目详情

已知a2-3a+1=0,则a4+
1
a4
=______.
题型:填空题难度:偏易来源:不详

答案

∵a2-3a+1=0,
∴a-3+class="stub"1
a
=0,
即a+class="stub"1
a
=3,
两边平方得,a2+2+class="stub"1
a2
=9,
∴a2+class="stub"1
a2
=7,
再平方得,a4+2+class="stub"1
a4
=49,
∴a4+class="stub"1
a4
=47.
答案为:47.

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