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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