This is irrational!

If x,x, y,y, x2,x^2, y2y^2 and xyxy are all irrational, is it possible that more than one of xy,x-y, x+y,x+y, x2y2,x^2-y^2, and x2+y2x^2+y^2 is rational?

Assume that xx and yy are real numbers with different absolute values.

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