In this multi-part problem, we will consider this system of simultaneous equations:
5xy-10yz-6xz = -41,
xyz = 6.
Let a=3x, b=5y and c=-6z .
(A) Determine the monic cubic polynomial in terms of a variable t whose roots are ,t=a, t=b, and t=c.
The answer to A is t^3 - 2 t^2 - 123 t + 540 so I only need help with B
(B0 Given that (x,y,z) is a solution to the original system of equations, determine all distinct possible values of x+y.
Using the cubic, the solutions to the original system are (3,1,2) and (-4,1,-3/2), so the possible values of x + y are 4 and -3.