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MathNet 2015-part-07 — 185 problems (EN–VI) Question 139

Math Olympiad Vault · MathNet 2015-part-07 — 185 problems (EN–VI)

Question 139

The complex numbers $x, y, z$ satisfy
$$
\begin{aligned}
x y z & = -4 \\
(x+1)(y+1)(z+1) & = 7 \\
(x+2)(y+2)(z+2) & = -3
\end{aligned}
$$
Find, with proof, the value of $(x+3)(y+3)(z+3)$.