Two different positive numbers $a$ and $b$ each differ from their reciprocals by $1$. What is $a+b$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Two different positive numbers $a$ and $b$ each differ from their reciprocals by $1$. What is $a+b$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{5}
Two different positive numbers $a$ and $b$ each differ from their reciprocals by $1$. What is $a+b$?
train