# Expand to seek trouble

Algebra Level 5

${\left| \begin{matrix} { \left( a-x \right) }^{ 2 } & { \left( a-y \right) }^{ 2 } & { \left( a-z \right) }^{ 2 } \\ { \left( b-x \right) }^{ 2 } & { \left( b-y \right) }^{ 2 } & { \left( b-z \right) }^{ 2 } \\ { \left( c-x \right) }^{ 2 } & { \left( c-y \right) }^{ 2 } & { \left( c-z \right) }^{ 2 } \end{matrix} \right| =-\frac { 351 }{ 8 } }$

If $$x,y,z$$ are roots of the equation $${8X^3-62X^2+43X-7=0}$$, and they satisfy the determinant above, where $$a,b$$ and $$c$$ are distinct numbers, find the value of $$|(a-b)(b-c)(c-a)|$$.

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