a's, b's and c's

Algebra Level 2

If \(a+b+c = 0\) and \( abc \neq 0 \), then find the value of \( \frac { { a }^{ 4 } + { b }^{ 4 } + { c }^{ 4 } } { { a }^{ 2 }{ b }^{ 2 }+ { b }^{ 2 }{ c }^{ 2 }+ { c }^{ 2 }{ a }^{ 2 } } \).

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