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An interesting problem on monotonicity

Find the number of solutions of the equation x+y=xe^y+ye^x

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We have x+y=xe^y+ye^x
clearly x=y=0 is a solution.
If xy>0 then both sides are positive, hence there will be no solution.
So, let ...

Solution Summary

In this solution, a logical way of finding the solutions of a given equation involving two variables is discussed. Monotonicity of the function involved is used to come to the conclusion.