# 1729

Algebra Level 5

$\begin{eqnarray} abc+ab+bc+ca+a+b+c&=&1\\ bcd+bc+cd+db+b+c+d&=&7 \\ cda+cd+da+ac+c+d+a&=&2\\ dab+da+ab+bd+d+a+b&=&9 \end{eqnarray}$

There exist 4 non-real numers$$a,b,c$$ and $$d$$ satisfying the system of equations above, find the value of $$((a-b)(a-d)(c-b)(c-d))^3$$.