Solving a tricky sum of square roots (Olympiad practice)

Thanks to Devesh from India for the suggestion! A version of this problem was given in an Olympiad qualifying test.

Socratic
https://socratic.org/questions/a-root-a-b-root-b-183-a-root-b-b-root-a-182-find-9-5-a-b
Math StackExchange
https://math.stackexchange.com/questions/2405256/find-the-value-of-frac95ab-given-that-a-sqrtab-sqrtb-183-and-a
Brainly
https://brainly.in/question/3901575
Quora
https://www.quora.com/Suppose-a-b-are-positive-real-numbers-such-that-a%E2%88%9Aa-+-b%E2%88%9Ab-183-a%E2%88%9Ab-+-b%E2%88%9Aa-182-How-do-we-find-9-5-a-+-b

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