The Other Way Around

Algebra Level 4

\[ \begin{eqnarray} a+b+c &=&1\\ a^2+b^2+c^2 &=& 2\\ a^3+b^3+c^3 &=& 3\\ \end{eqnarray} \]

Numbers \(a,b,c\) satisfy the equations above.

What is the value of \({ a }^{ -1 }+{ b }^{ -1 }+{ c }^{ -1 } \)?

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