Let $x$ and $y$ be real numbers such that $2(x^2 + y^2) = x + y.$  Find the maximum value of $x - y.$
Question:
Let $x$ and $y$ be real numbers such that $2(x^2 + y^2) = x + y.$  Find the maximum value of $x - y.$
Answer:
Let's think step by step.

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\frac{1}{2}
Let $x$ and $y$ be real numbers such that $2(x^2 + y^2) = x + y.$  Find the maximum value of $x - y.$
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