问题 选择题
If a<b<0,then the following inequality must be hold(  )
(英语小词典:following:下面的;inequality:不等式)
A.
1
a
1
b
B.
1
|a|
1
|b|
C.
1
a-b
1
a
D.(b+
1
a
)2
(a+
1
b
)2
答案

∵a<b<0,

∴设a=-2,b=-1,

A、∵

1
a
=-
1
2
1
b
=-1,∵-
1
2
>-1,∴
1
a
1
b
,故本选项错误;

B、∵

1
|a|
=
1
2
1
|b|
=1,
1
2
<1,∴
1
|a|
1
|b|
,故本选项错误;

C、∵

1
a-b
=
1
-2+1
=-1,
1
a
=-
1
2
,-1<-
1
2
,∴
1
a-b
1
a
,故本选项错误;

D、∵(b+

1
a
)2=(-1+
1
-2
)
2
=
9
4
(a+
1
b
)
2
=(-2+
1
-1
)
2
=9,
9
4
<9,∴(b+
1
a
)2
(a+
1
b
)2
,故本选项正确.

故选D.

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