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 \( ((a-b)(a-d)(c-b)(c-d))^3\).


please try its sequel here

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