# Cyclic Inequality!

Algebra Level 5

$\large{\dfrac{x}{\sqrt{y^2 + z^2}} + \dfrac{y}{\sqrt{z^2 + x^2}} + \dfrac{z}{\sqrt{x^2 + y^2}} > A}$ If the largest real number $$A$$ such that the above inequality is true for all possible positive real numbers $$x,y,z$$ can be expressed as $$\dfrac{\alpha}{\sqrt{\beta}}$$, where $$\alpha, \beta$$ are positive integers, find the minimum value of $$\alpha \beta$$.

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