$1 \cdot 103$ Given the equation $\sqrt{a(x-a)}+\sqrt{a(y-a)}=\sqrt{x-a}-\sqrt{a-y}$ holds in the real number range, where $a, x, y$ are distinct real numbers, then the value of $\frac{3 x^{2}+x y-y^{2}}{x^{2}-x y+y^{2}}$ is
(A) 3.
(B) $\frac{1}{3}$.
(C) 2.
(D) $\frac{5}{3}$.
(China Junior High School Mathematics League, 1991)
［Solution］ According to the properties of arithmetic roots, from the right end we know that there must be $y<a<x$, and from the left end we know that there must also be $a \geqslant 0$ and $a \leqslant 0$. Therefore, it must be that $a=0$.
From this, we can deduce that $x=-y$. Thus,
$$
\frac{3 x^{2}+x y-y^{2}}{x^{2}-x y+y^{2}}=\frac{3 y^{2}-y^{2}-y^{2}}{y^{2}+y^{2}+y^{2}}=\frac{1}{3} .
$$

Therefore, the answer is $(B)$.