# Problem 41

Algebra Level 4

$\large S = \sqrt{x^2+\dfrac{1}{y^2}}+\sqrt{y^2+\dfrac{1}{z^2}}+\sqrt{z^2+\dfrac{1}{x^2}}$

Given that $$x,y$$ and $$z$$ are non-zero reals. Let the minimum value of $$S$$ be $$S_{\min}$$. Find $$(S_{\min})^2$$.

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