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Algebra Level 4

\[ x^4 + y^4 + z^4 - 4 xyz = -1 \]

Find the sum of all possible values of \(x,y,z\) where \(x,y,z\) are real numbers.

  • Ex. if there are two pairs of values then sum of values of \(x,y,z\) is \((2,3,4) , (1,2,-3)\) here sum is \(2+3+4+1+2-3\)
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