已知 x=n+1−nn+1+nx=\dfrac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}x=n+1+nn+1−n, y=n+1+nn+1−ny=\dfrac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}-\sqrt{n}}y=n+1−nn+1+n,且 19x2+123xy+19y2=198519x^2+123xy+19y^2=198519x2+123xy+19y2=1985.试求正整数nnn.
