# Don't make mistake

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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