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Question

Solution set of the equation xx1+|x|=x2|x1| is :


A

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B

( 1 , )

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C

( 0 , )

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D

{0} ( 1 , )

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Solution

The correct option is D

{0} ( 1 , )


xx1+|x|=x2x1 = x(x1)+xx1

xx1+x+|x|=xx1

x.xx1 0 x> 1 or x=0

Hence solution is {0} ( 1 , ).

Here we use the fact that |a+b| = |a| + |b|

if a and b are of same sign i.e., ab > 0.


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