已知x+1x=2,则下列等式成立的有()①x2+1x2=2;②x4+1x4=2;③x8+1x8=2;④x-1x=0.A.①B.①②C.①②③D.①②③④-数学

题目简介

已知x+1x=2,则下列等式成立的有()①x2+1x2=2;②x4+1x4=2;③x8+1x8=2;④x-1x=0.A.①B.①②C.①②③D.①②③④-数学

题目详情

已知x+
1
x
=2
,则下列等式成立的有(  )
x2+
1
x2
=2
;②x4+
1
x4
=2
;③x8+
1
x8
=2
;④x-
1
x
=0
A.①B.①②C.①②③D.①②③④
题型:单选题难度:偏易来源:不详

答案

∵x+class="stub"1
x
=2,
∴x2+class="stub"1
x2
=(x+class="stub"1
x
)2-2•x•class="stub"1
x
=22-2=2,∴①正确;
x4+class="stub"1
x4
=(x2+class="stub"1
x2
)2-2•x2•class="stub"1
x2
=22-2=2,∴②正确;
x8+class="stub"1
x8
=(x4+class="stub"1
x4
)2-2=2,∴③正确
(x-class="stub"1
x
)2=(x+class="stub"1
x
)2-4•x•class="stub"1
x
=22-4=0,∴④正确;
故选D.

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