> 数学 >
已知a2-3a+1=0,则a4+
1
a4
=______.
人气:329 ℃ 时间:2020-04-05 16:30:19
解答
∵a2-3a+1=0,
∴a-3+
1
a
=0,
即a+
1
a
=3,
两边平方得,a2+2+
1
a2
=9,
∴a2+
1
a2
=7,
再平方得,a4+2+
1
a4
=49,
∴a4+
1
a4
=47.
答案为:47.
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