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2023 WSMO Speed Round Problems/Problem 9

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Problem

Suppose that $b$ and $c$ are the roots of the equation $x^2-\log(16)x+\log(64).$ If $\sqrt{a+b}+\sqrt{a+c} = \sqrt{b+c},$ then $2^a = \frac{\sqrt{m}}{n},$ find $m+n.$

Solution

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