已知x2-3x+1=0,则x-1x=______.-数学

题目简介

已知x2-3x+1=0,则x-1x=______.-数学

题目详情

已知x2-3x+1=0,则x-
1
x
=______.
题型:填空题难度:中档来源:不详

答案

已知等式变形得:x+class="stub"1
x
=3,
两边平方得:(x+class="stub"1
x
)2=x2+2+class="stub"1
x2
=9,即x2+class="stub"1
x2
=7,
则(x-class="stub"1
x
)2=(x+class="stub"1
x
)2-2=7-2=5,
则x-class="stub"1
x
5

故答案为:±
5

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