Suppose \( a, b, c \) are distinct and \( x, y, z \) are connected ...

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Suppose \( a, b, c \) are distinct and \( x, y, z \) are connected by the system of equations
\[
\begin{array}{l}
x+a y+a^{2} z=a^{3} \\
x+b y+b^{2} z=b^{3} \\
x+c y+c^{2} z=c^{3}
\end{array}
\]
then
(a) \( a+b+c \)
(p) \( x \)
(b) \( b c+c a+a b \)
(q) \( -y \)
(c) \( a b c \)
(r) \( z \)
(d) \( (b+c)(c+a)(a+b) \)
(s) \( -(x+y z) \)
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