$2 \cdot 17$ If $x_{1}, x_{2}$ are two distinct real roots of the equation $x^{2}+2 x-k=0$, then $x_{1}^{2}+x_{2}^{2}-2$ is
(A) a positive number.
(B) a negative number.
(C) zero.
(D) a number not greater than 0.
(China Beijing Junior High School Mathematics Competition, 1992)
［Solution］ Given that the equation has two distinct real roots, then
$$
\begin{aligned}
\Delta=2^{2}+4 k>0, & \text { so } \quad k>-1 . \\
\therefore \quad x_{1}^{2}+x_{2}^{2}-2 & =\left(x_{1}+x_{2}\right)^{2}-2 x_{1} x_{2}-2 \\
& =4+2 k-2=2+2 k>0 .
\end{aligned}
$$

Therefore, the answer is $(A)$.