Question 51
Find all triples $(x, y, z)$ of positive integers such that
$$
\sqrt{\frac{2005}{x+y}} + \sqrt{\frac{2005}{x+z}} + \sqrt{\frac{2005}{y+z}}
$$
is a positive integer.
$$
\sqrt{\frac{2005}{x+y}} + \sqrt{\frac{2005}{x+z}} + \sqrt{\frac{2005}{y+z}}
$$
is a positive integer.