Generalizing stuff

Algebra Level 3

Given that \(a_1,a_2,\ldots,a_n,b_1,b_2,\ldots,b_n\) are non-negative real numbers that sum to 10, find the minimum possible value of \[\left( \sum_{i=1}^{n} \sqrt{a_i^2+b_i^2}\right)^2.\]

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