问题 选择题
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
答案

∵x+

1
x
=2,

∴x2+

1
x2
=(x+
1
x
2-2•x•
1
x
=22-2=2,∴①正确;

x4+

1
x4
=(x2+
1
x2
2-2•x2
1
x2
=22-2=2,∴②正确;

x8+

1
x8
=(x4+
1
x4
2-2=2,∴③正确

(x-

1
x
2=(x+
1
x
2-4•x•
1
x
=22-4=0,∴④正确;

故选D.

判断题
问答题