Let a,b be the roots of the square trinomial f(x)=x2−2x−1, and c,d be the roots of the square trinomial g(x)=x2−3x−1.
The minimum value of g3(a)f(c)+g3(b)f(d) can be expessed in the form m+nl, where m,n,l are integers and l is a free-square number.
Find m+n+l.