SAMO Problem 3: Solution to system of polynomial equations
Source: South African Mathematics Olympiad 2020, Problem 3
January 17, 2021
algebrapolynomialsystem of equations
Problem Statement
If , , are real numbers satisfying
\begin{align*}
(x + 1)(y + 1)(z + 1) & = 3 \\
(x + 2)(y + 2)(z + 2) & = -2 \\
(x + 3)(y + 3)(z + 3) & = -1,
\end{align*}
find the value of