If ^ -1 x+ ^ -1 y= 2 3 , ^ -1 x- ^ -1 y= 3 then the number of values of (x,y) is

JEE Advanced Mathematics question

If , then the number of values of is

Answer: (D)

Let , ; then and . The equations become

A+B=, (-A)-(-B)=B-A=.

This linear system has the unique solution ,

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Question ID VK-108640