The number of real roots of |x|^3 – 3(x)^2 + 3|x| – 2 =0 is

1)1

2)2

3)3

4)none of these

By differentiating ,equation becomes          3x^2-6x+3=3*(x-1)*(x-1).

So,at x =1, the above eq will be zero and hence it will be a turning point for the graph of the given equation.

As( x-1) is occurring twice ,it can be considered two turning points(actually one meet ing at same place on graph of the eq.mentinoned in the question.

So as their are 2 turning points , 

 

Number of real roots= turning points +1 

                                     =2+1=3