Let $$x$$ and $$y$$ be two real variables such that $$x>0$$ and $$xy=1$$. Find the minimum value of $$x+y$$.

Prove that the minimum value of $${{\left( {a + x} \right)\left( {b + x} \right)} \over {\left( {c + x} \right)}},$$
$$a,b > c,x > - c$$ is $${\left( {\sqrt {a - c} + \sqrt {b - c} } \right)^2}$$.