# Fascinating minima

Algebra Level 3

$\large \left (x+\dfrac{1}{y}\right)^2+\left(y+\dfrac{1}{z}\right)^2+\left(z+\dfrac{1}{x}\right)^2$

If $$x,y$$ and $$z$$ are are positive numbers satisfying $$x+y+z=6$$, find the minimum value of expression above.

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