# 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 \((S_{\min})^2 \).

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

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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