已知,x2-5x-1=0,求:(1)x2+1x2(2)2x2-5x+1x2.-数学

题目简介

已知,x2-5x-1=0,求:(1)x2+1x2(2)2x2-5x+1x2.-数学

题目详情

已知,x2-5x-1=0,求:
(1)x2+
1
x2

(2)2x2-5x+
1
x2
题型:解答题难度:中档来源:不详

答案

(1)∵x2-5x-1=0,
∴x-5-class="stub"1
x
=0,
∴x-class="stub"1
x
=5,
∴两边平方得:x2-2+class="stub"1
x2
=25,
x2+class="stub"1
x2
=27.
(2)∵x2-5x-1=0,
∴x2-5x=1,
∴2x2-5x+class="stub"1
x2
=x2-5x+x2+class="stub"1
x2
=1+27=28.

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