# Come and See this Nice Real System

Algebra Level 5

Let $$(a_1,b_1)$$, $$(a_2,b_2)$$, ..., $$(a_n,b_n)$$ be all the pairs of real numbers that satisfy following system of equations:$\left\{\begin{matrix} a^3+6ab+8= b^3 \\a^5+32= b^5 \end{matrix}\right.$ Find the value of$n+\sum_{k=1}^{n} (a_k^2+b_k^2) \ .$

###### This problem is original and belongs to this set.
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