2.22 Given that $p$ and $q$ are rational numbers, and $x=\frac{\sqrt{5}-1}{2}$ satisfies $x^{3}+p x+q=0$. Then the value of $p+q$ is
(A) -1.
(B) 1.
(C) -3.
(D) 3.
(Anhui Province, China Junior High School Mathematics Competition, 1997)
[Solution] Substituting $x=\frac{\sqrt{5}-1}{2}$ into $x^{3}+p x+q=0$, simplifying yields $4 \sqrt{5}(2+p)+4(2 q-p-4)=0$. Since $p, q$ are rational numbers, we have
$$
\left\{\begin{array}{l}
2+p=0, \\
2 q-p-4=0 .
\end{array}\right.
$$

Solving these equations gives $p=-2, q=1$. Therefore, $p+q=-1$. Hence, the answer is $(A)$.