Generalizing stuff

Algebra Level 3

Given that a1,a2,,an,b1,b2,,bna_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 (i=1nai2+bi2)2.\left( \sum_{i=1}^{n} \sqrt{a_i^2+b_i^2}\right)^2.

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