Problem 2 Let xxx , yyy , zzz be positive reals satisfying (x+y+z)3=32xyz\left(x+y+z\right)^{3}=32xyz(x+y+z)3=32xyz Find the minimum and the maximum of P=x4+y4+z4(x+y+z)4P=\frac{x^{4}+y^{4}+z^{4}}{\left(x+y+z\right)^{4}}P=(x+y+z)4x4+y4+z4