It may be complex

Algebra Level 4

Let $$a$$, $$b$$ and $$c$$ be roots of the polynomial $$P(x)=x^3-2x^2+3x-4$$. Determine

$\large \left(a+\dfrac{1}{a}\right)\left(b+\dfrac{1}{b}\right)\left(c+\dfrac{1}{c}\right).$

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