Improved fewnomial upper bounds from Wronskians and dessins d'enfant

We use Grothendieck's dessins d'enfant to show that if P and Q are two real polynomials, any real function of the form x^ (1-x) ^ P - Q, has at most P + Q + 2 roots in the interval ]0, ~1[. As a consequence, we obtain an upper bound on the number of positive solutions to a real polynomial system f=g=0 in two variables where f has three monomials terms, and g has t terms. The approach we adopt for tackling this Fewnomial bound relies on the theory of Wronskians, which was used in Koiran et. \ al. \ (J. \ Symb. \ Comput. , 2015) for producing the first upper bound which is polynomial in t.