1.101 Let $x_{1} \geqslant x_{2} \geqslant 0, x_{1}+x_{2}=2$. Then
$$
\sqrt{x_{1}+\sqrt{x_{1}{ }^{2}-x_{2}{ }^{2}}}+\sqrt{x_{1}-\sqrt{x_{1}{ }^{2}-x_{2}{ }^{2}}}
$$

equals
(A) 2 .
(B) 0 .
(C) $x_{1}-x_{2}$.
(D) Cannot be determined.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991)
[Solution] $(\text { Original })^{2}=x_{1}+\sqrt{x_{1}^{2}-x_{2}^{2}}+x_{1}-\sqrt{x_{1}^{2}-x_{2}^{2}}$
$$
\begin{aligned}
& +2 \sqrt{\left(x_{1}+\sqrt{x_{1}^{2}-x_{2}^{2}}\right)\left(x_{1}-\sqrt{x_{1}^{2}-x_{2}^{2}}\right)} \\
= & 2 x_{1}+2 x_{2}=2\left(x_{1}+x_{2}\right)=4,
\end{aligned}
$$
$\therefore \quad$ Original $=2$.
Therefore, the correct choice is $(A)$.