Olympiad selection grade 10th part II

Algebra Level 4

\[\large x^2y^3+y^2z^3+z^2x^3+(x-1)^2+(y-1)^2+(z-1)^2\]

Given that \(x,y\) and \(z\) are positive reals satisfying \(xy+yz+xz=3\), find the minimum value of the expression above.

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