Problem 41

Algebra Level 4

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}}

Given that x,yx,y and zz are non-zero reals. Let the minimum value of SS be Smin⁡ S_{\min} . Find (Smin⁡)2(S_{\min})^2 .

This problem has been taken from Azerbaijan TST prepare for IMO 2016.
For more inequality problems, see this set: It's all about the inequality.
Son Nguyen by Son Nguyen
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