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Question

The inequality |x|2|x|22|x||x|22>0 holds if and only if

A
1<x<23 or 23<x<1
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B
none of these
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C
23<x<1
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D
2<x<2
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Solution

The correct option is D 2<x<2
Let |x|=t
t2t22tt22>0
(t2)(t+1)t22t+2<0
(t2)(t+1)((t1)2+1)<0

Here (t1)2+1>0 t R

(t2)(t+1)<0
1<t<2
1<|x|<2
2<x<2

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