Question:
If $x \neq y \neq z$ and $\left|\begin{array}{lll}x & x^{3} & x^{4}-1 \\ y & y^{3} & y^{4}-1 \\ z & z^{3} & z^{4}-1\end{array}\right|=0$, prove that $x y z(x y+y z+z x)=(x+y+z)$
Solution:
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