Let $x$ and $y$ be nonzero real numbers such that
\[xy(x^2 - y^2) = x^2 + y^2.\]Find the minimum value of $x^2 + y^2.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be nonzero real numbers such that
\[xy(x^2 - y^2) = x^2 + y^2.\]Find the minimum value of $x^2 + y^2.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Let $x$ and $y$ be nonzero real numbers such that
\[xy(x^2 - y^2) = x^2 + y^2.\]Find the minimum value of $x^2 + y^2.$
train