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Unless I am reading something wrong , I do not think we can anser this question with the information provided :

xy=1 then what is the value of [2(x+y)^2] / [2(x-y)^2]

lets consider 2 sets of values for x and Y (2,1/2) and (3,1/3)

the value for the 1st expression will be = [2(x+y)^2] / [2(x-y)^2] =[ 1.5^2/.5^2]=9

the valuse for the 2nd set will be = [ 1.33^2 / .67^2 ] = 4

so the valuse can be anything unless some more information is given.. can you please check that you have written the expression correctly [2(x+y)^2] / [2(x-y)^2]

I wrote the question as it appeared. When I saw this question first thing that popped up in my mind was THIS QUESTION IS ABNORMAL. Indeed, we cannot solve it with the given structure.

I have seen this question with the format what zoinnk has mentioned. However, if the question is as mentioned originally, and if it asks "what could be the value", I will approach it as below.