An algebra problem by Kshetrapal Dashottar

Algebra Level 4

\(x,y,z\) are real numbers such that \(x + y + z = 3\) and \(xy + yz + zx = a\) (where \(a\) is real parameter). Determine the value of \(a\) for which the difference between the maximum and minimum possible value of \(x\) is equal to 8.

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