This is irrational!

If \(x,\) \(y,\) \(x^2,\) \(y^2\) and \(xy\) are all irrational, is it possible that more than one of \(x-y,\) \(x+y,\) \(x^2-y^2,\) and \(x^2+y^2\) is rational?

Assume that \(x\) and \(y\) are real numbers with different absolute values.

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