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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