A little long recursion RELOADED

Algebra Level 5

If \(a\), \(b\) and \(c\) are complex numbers such that:

\[a^2+b^2+c^2=25\] \[a^3+b^3+c^3=106\] \[a^4+b^4+c^4=477\] \[a+b+c \in N\]

Then we let: \[x+y+z=\sqrt{a^5+b^5+c^5+17}\] \[xy+xz+yz=\sqrt{a^7+b^7+c^7-42}\] \[xyz=\sqrt{a^6+b^6+c^6+51}\]

Find \(\lfloor \sqrt{|(x-y)(y-z)(z-x)|} \rfloor\).

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