Again Minimum

Algebra Level 4

\[\displaystyle \sum_{cyc}^{a,b,c}\left[\frac{a^{2}+b^{2}}{ab}\right]\]

If \(a,b,c\) be the roots of \(x^{3}+(\omega^{4}+4\omega^{2}+1)x=x^{2}+\omega^{2}\), where \(\omega\) is some real number, then find the minimum value of the above expression.

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