己知实数x满足x+1x=3,又x3+mx2+xx4+2mx2+1=13,则m=()A.-2B.-1C.1D.2-数学

题目简介

己知实数x满足x+1x=3,又x3+mx2+xx4+2mx2+1=13,则m=()A.-2B.-1C.1D.2-数学

题目详情

己知实数x满足x+
1
x
=3,又
x3+mx2+x
x4+2mx2+1
=
1
3
,则m=(  )
A.-2B.-1C.1D.2
题型:单选题难度:中档来源:不详

答案

∵x+class="stub"1
x
=3,
∴x2+1=3x,x2+2+class="stub"1
x2
=9,
∴x4+1=7x2,
x3+mx2+x
x4+2mx2+1
=
x(x2+1)+mx2
7x2+2mx2
=
3x2+mx2
7x2+2mx2
=class="stub"3+m
7+2m
=class="stub"1
3

∴9+3m=7+2m,
解得m=-2.
故选A.

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