An algebra problem by Dinesh Chavan

Algebra Level 3

Let \(x,y,z\) be positive real numbers.

Given that \(xyz=1\)

Then find the minimum value of

\(\frac{1}{x^2+3x+2}+\frac{1}{y^2+3y+2}+\frac{1}{z^2+3z+2}\)

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