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In this multi-part problem, we will consider this system of simultaneous equations:
3x+5y-6z =2, 
5xy-10yz-6xz = -41, 
xyz = 6. 

Let a=3x, b=5y and c=-6z .

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(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.

 Jun 14, 2021
 #1
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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.

 Jun 14, 2021
 #2
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I believe the answer is 4 and -3

 

I hope this helps!

 Jun 17, 2021

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