+349 In this multi-part problem, we will consider this system of simultaneous equations:
3x + 4y + 30z = -60,
2xy + 42xz - 16yz = 68,
5xyz = 56.
Let a = x/2, b = 5y and c = -4z.
Determine the monic cubic polynomial in terms of a variable t whose roots are t = a, t = b, and t = c.
[i]This is a continuation of the problem above.[/i]
Given that $(x,y,z)$ is a solution to the original system of equations, determine all distinct possible values of $x + y + z$.
(Suggestion: Using the substitutions in part (a), first determine all possible values of the ordered triple $(a,b,c)$, then determine the possible solutions $(x,y,z)$.)
