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Algebra Level 3

\[\large \left(\dfrac{a^2+b^2}{c^2}\right)\left[\left(\dfrac{a^3+b^3+c^3}{abc}\right)^6 - 29\right]\]

Consider a polynomial such that its roots are in arithmetic progression and the squares of these roots are also in an arithmetic progression in the same order.

If the roots are \(a,b,c\) such that \(a,b,c \neq 0\) , find the value of the said expression above.

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