1. Let the equation $\sqrt{a(x-a)}+\sqrt{a(y-a)}=\sqrt{x-a}-\sqrt{a-y}$ hold in the real number range, where $a, x, y$ are pairwise 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) $\frac{5}{3}$.
1. (B)

Solution According to the properties of arithmetic roots, from the right side we know $y<a<x$, and from the left side we know $a \geqslant 0$ and $a \leqslant 0$, so $a=0$.
This leads to $x=-y$, substituting into the required expression yields a value of $\frac{1}{3}$.