已知x-1x=1,则x2+1x2=______.-数学

题目简介

已知x-1x=1,则x2+1x2=______.-数学

题目详情

已知x-
1
x
=1,则x2+
1
x2
=______.
题型:填空题难度:中档来源:不详

答案

方法一:∵x-class="stub"1
x
=1,
∴(x-class="stub"1
x
)2=1,
即x2+class="stub"1
x2
-2=1,
∴x2+class="stub"1
x2
=3.

方法二:∵x-class="stub"1
x
=1,
∴x2+class="stub"1
x2
=(x-class="stub"1
x
)2+2,
=12+2,
=3.

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