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Question

Solution set of the inequation (x1|x|)<0, is

A
[1,1+52)
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B
[1,1]
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C
[1,1+52]
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D
(1,1+52)
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Solution

The correct option is C [1,1+52)
Given,

x1+|x|<0
x<1|x|x2<1 for x>0
x2<1|x|=1x.
x2+x1<0
x=1±14(1)2=1+52 ...(1)
And 1|x| is defined where
1|x||x|1
1x1
x[1,1+52)

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