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 \(A+a+b\).

Write your answer to 3 decimal places.

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