2・103 If $a \neq b, a^{3}-b^{3}=19 x^{3}$ and $a-b=x$, which of the following conclusions is correct?
(A) $a=3 x$.
(B) $a=3 x$ or $a=-2 x$.
(C) $a=-3 x$ or $a=2 x$.
(D) $a=3 x$ or $a=2 x$.
(E) $a=2 x$.
(26th American High School Mathematics Examination, 1975)
[Solution] If $a \neq b, \quad a^{3}-b^{3}=19 x^{3}$, and $a-b=x$, then $a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)=x\left(a^{2}+a b+b^{2}\right)=19 x^{3}$.
Divide the last equation by $x$ and substitute $b=a-x$ into the equation to get $\square$
$$
\begin{array}{c}
18 x^{2}+3 a x-3 a^{2}=0, \\
-3(a-3 x)(a+2 x)=0,
\end{array}
$$

Solving gives
$$
a=3 x \text { or } a=-2 x \text {. }
$$

Therefore, the answer is $(B)$.