# How do I factor each of these?

$\begin{eqnarray} ab+cd&=&38 \\ ac+bd&=&34\\ ad+bc&=&43\\ \end{eqnarray}$

Let $$a,b,c$$ and $$d$$ positive integers such that they satisfy the system of equations above. Find $$a+b+c+d$$.

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