If x^3+y^3+z^3 = x^2+y^2+z^2 = x+y+z = 1 then what would be the max value of xyz?

Question

x, y, z and k are four non zero positive integers satisfying 1/x + y/2 = z/3 + 4/k, minimum integral value of k for integral value of x, y and z will be

Answer 1

If x^3+y^3+z^3 = x^2+y^2+z^2 = x+y+z = 1,

There could be 3 possibilities.

(1) x=0, y=0, z=1
(2) x=0, y=1, z=0
(3) x=1, y=0, z=0

So, max value of xyz=1