Discussing an unpublished approach of a former team member
I need to justify...why I decided to use MY approach and NOT X's approach. 


I don't think you need any such justification: "[X's approach] does not work....nothing has been published by him." Thus, the literature contains nothing about X's work and you need not compare your results to his unpublished work. Nonetheless, if you feel that some reference to his work is necessary, then you could mention that X is working on the topic or that some of your ideas followed from discussions with X or ...


  It's...interesting...to know...why X's approach...does not work.


Many approaches don't work. You cannot possibly mention them all. It is perfectly reasonable to omit discussion of X's approach. That said, in some cases -- e.g., when the obvious solution seems feasible -- you might like to very briefly mention why the obvious solution doesn't work. For instance, you could mention: This problem can be intuitively solved by ABC, however, ... (You could also mention that X pursued some of these ideas, or that you pursued some of these ideas with X.)