(x+y+z)4x4+y4+z4
Let the minimum and maximum values of the above expression be α and β, respectively, satisfying the following conditions:
- x,y,z∈R+
- (x+y+z)3=32xyz.
Suppose α can be represented as DA−BC, and β as FE, for positive integers A,B,C,D,E,F and with C having no square factors.
Then find the minimum value of A+B+C+D+E+F.