# 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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