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Suppose a ,b ,c in I such that the grea...

Suppose `a ,b ,c in I` such that the greatest common divisor of `x^2+a x+b and x^2+bx+c is (x+1)` and the least common multiple of `x^2+a x+b and x^2+b x+c` is `(x^3-4x^2+x+6)dot` Then the value of `|a+b+c|` is equal to ___________.

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