Sum of powers

Algebra Level 3

{a+b+c=1a2+b2+c2=21a3+b3+c3=55 \begin{cases} a+b+c=1\\ { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=21\\ { a }^{ 3 }+{ b }^{ 3 }+{ c }^{ 3 }=55 \end{cases}

Given that a,ba,b and cc satisfy the system of equations above, find (a1)(b1)(c1)(a-1)(b-1)(c-1) .

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