Let b be the burn fee, a ratio.
_f signifies final balance of a token held in Behodler at the end of a trade.
_i signifies initial balance of the token.
I is input token and O is for output token.
Therefore, I_f is the final balance of input token.
The exchange equation is then:
√F(√I_f - √I_i) = (√O_i - √O_f)/(F)