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

×