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Let a,b,ca, b, ca,b,c be complex numbers satisfying a+b+c=abc=1a + b +c = abc = 1a+b+c=abc=1
and ab+bc+ac3=1a2+1b2+1c2\dfrac{ab+bc+ac}{3} = \dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}3ab+bc+ac=a21+b21+c21
The sum of absolute values of all possible ab+ac+bcab + ac + bcab+ac+bc can be written as nm\dfrac{\sqrt{n}}{m}mn , where nnn and mmm are positive coprime integers. What is the value of n+mn + mn+m ?
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