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________

Answer

6

Explanation

`x^(3)-x^(2)-1=0 to alpha, beta, gamma implies alpha^(2)+beta^(2)+gamma^(2)=1`
`alpha^(2)+beta^(3)+gamma^(4)=alpha^(2)+beta^(2)+1+gamma^(3)+gamma=3+gamma`
In given equation `x to x-3impliesx^(3)-10x^(2)+33x-37=0`