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2023 WSMO Speed Round Problems/Problem 9

Revision as of 14:34, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Suppose that <math>b</math> and <math>c</math> are the roots of the equation <math>x^2-\log(16)x+\log(64).</math> If <math>\sqrt{a+b}+\sqrt{a+c} = \sqrt{b+c},</ma...")
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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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