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If x^(3)+ax^(2)+bx+c=0 has the roots alp...

If `x^(3)+ax^(2)+bx+c=0` has the roots `alpha^(2)+beta^(3)+gamma^(4),beta^(2)+gamma^(3)+alpha^(4)` and `gamma^(2)+alpha^(3)+beta^(4)` where `alpha, beta, gamma` are the roots of `x^(3)-x^(2)-1=0` then the value of `a+b+c` is equal to________

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