Given that x^2 - 4x + 8 = 0, find the value(s) of x?

Question

If
x, y, z are 3 non zero positive integers such that x+y+z = 8 and xy+yz+zx = 20,
then
What would be minimum possible value of x*y^2*z^2

Answer 1

2+2i and 2-2i