Do you know Soumava's Algorithm?

Calculus Level 3

xy=yx=43 \large x^y = y^x = 43

If xx and yy are distinct positive real numbers satisfying the equation above, find 100(x+y)\lfloor 100(x+y) \rfloor .

You are allowed to use computer assistance.

You might refer to Soumava's algorithm.

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