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S=x2+1y2+y2+1z2+z2+1x2\large S = \sqrt{x^2+\dfrac{1}{y^2}}+\sqrt{y^2+\dfrac{1}{z^2}}+\sqrt{z^2+\dfrac{1}{x^2}}S=x2+y21+y2+z21+z2+x21
Given that x,yx,yx,y and zzz are non-zero reals. Let the minimum value of SSS be Smin S_{\min} Smin. Find (Smin)2(S_{\min})^2 (Smin)2.
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