System of equations... Can YOU find \(n\)?

Algebra Level pending

\(x\), \(y\), and \(z\) are all real numbers.

\(x+y+z=0\)

\(x ^ 2+y ^ 2+z ^ 2=\sqrt{74}\)

\(x ^ 4+y ^ 4+z ^ 4=n\)

Find the value of \(\frac{n-7}{2}\).

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