A triple square root problem (Berkeley mini math tournament)

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Here's a beautiful radical equation with 3 square roots. We are going to find the sum of its solutions and there's a very fast way to do it (without using Vieta's formula) because this equation is well-designed. This math problem is from the Berkeley mini Math Tournament (BnMT) in 2021. This is a great practice and preparation for anyone who's interested in the math olympiad. For more info, please see https://www.ocf.berkeley.edu/~bmt/

0:00 a well-designed radical problem
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