# Difficult system of equations

Algebra Level 4

$\large { \begin{cases} a + \frac{a+8b}{a^2+b^2} = 2 \\ b + \frac{8a-b}{a^2+b^2} = 0 \end{cases} }$

If $$(a_1,b_1), (a_2,b_2) , \ldots ,(a_n,b_n)$$ are all the real solutions of $$(a,b)$$ which satisfy the system of equations above, find the value of $$\displaystyle \prod_{m=1}^n a_m b_m$$.

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