Positive real numbers $x,y$ satisfy the equations $x^2 + y^2 = 1$ and $x^4 + y^4= \frac{17}{18}$.  Find $xy$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Positive real numbers $x,y$ satisfy the equations $x^2 + y^2 = 1$ and $x^4 + y^4= \frac{17}{18}$.  Find $xy$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{6}
Positive real numbers $x,y$ satisfy the equations $x^2 + y^2 = 1$ and $x^4 + y^4= \frac{17}{18}$.  Find $xy$.
train