已知:a-1a=1,则a8+1a8=______.-数学

题目简介

已知:a-1a=1,则a8+1a8=______.-数学

题目详情

已知:a-
1
a
=1,则a8+
1
a8
=______.
题型:填空题难度:中档来源:不详

答案

∵a-class="stub"1
a
=1,∴(a-class="stub"1
a
)2=1,
∴a2-2×a×class="stub"1
a
+class="stub"1
a2
=1   即a2+class="stub"1
a2
=3,
∴(a2+class="stub"1
a2
)2=32,即a4+class="stub"1
a4
=9-2=7,
∴(a2+class="stub"1
a2
)4=72,即a8+class="stub"1
a8
=49-2=47,
故答案为47.

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