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Algebra Level 4

Given that \(a,b\) and \(c\) are real numbers satisfying \[\frac{1}{a^2+8}+\frac{1}{4b^2+8}+\frac{1}{9c^2+8}=\frac{1}{3}.\] Find the product of the minimum and maximum value of the expression below. \[a+2b+3c\]


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