# Division by 0? Nah

Algebra Level 5

Positive real numbers $$x$$ and $$y$$ are such that $$x>y$$ and $$xy=1$$. Find the minimum value of $$A=\dfrac { { x }^{ 2 }+{ y }^{ 2 } }{ x-y }$$.

If the answer can be expressed in the form of $$\sqrt [ a ]{ b }$$, where $$b$$ is a positive integer and $$a$$ is a positive real, find the minimum value of $$A+a+b$$.