# My Problem Number Six

Algebra Level 4

Let $$\mathcal R$$ be the set of real numbers and $$\mathcal S$$ the set of non-real complex numbers.

If $$a$$ is a positive real number and $$x, y$$ are in $$\mathcal R$$ or $$\mathcal S$$ such that $$x^{2}+y^{2}=4a^{2}$$, $$x+y=3a$$, then which of the following is true?

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