# Appropriate Substitution

Algebra Level 3

$x^3 - 6x^2 + 12x = 8$

If $$a,b,c$$ are the roots of the cubic equation above. And given that for coprime positive integers $$m,n$$, we have:

$\left ( \frac 1 a + \frac 1 b + \frac 1 c \right )^2 = \frac m n$

What is the value of $$16(m-n)$$?

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