# Bang, off with ya brain!

Algebra Level 5

$\large \begin{cases}{a_{1} + a_{2} + a_{3} + a_{4} + \ldots + a_{10} = 4} \\ {b_{1} + b_{2} + b_{3} + b_{4} + \ldots + b_{10} = -1}\end{cases}$

Let $$a_{1}, a_{2}, a_{3} , a_{4}, \ldots ,a_{10}$$ and $$b_{1}, b_{2}, b_{3} , b_{4}, \ldots ,b_{10}$$ be real numbers such that they satisfy the system of equations above.

What is the minimum positive value of the expression below? $\left(\sqrt{a_{1}^{2} + b_{1}^{2}} + \sqrt{a_{2}^{2} + b_{2}^{2}} + \ldots + \sqrt{a_{10}^{2} + b_{10}^{2}}\right)^{2}$

×