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2025 SSMO Accuracy Round Problems/Problem 3

Revision as of 11:26, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Nonnegative real numbers <math>x,y,</math> and <math>z</math> satisfy <cmath>\frac{\sqrt{x}+13}{y} = \frac{\sqrt{y}+29}{z} = \frac{\sqrt{z} + 46}{x} = 2</cmath> a...")
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Problem

Nonnegative real numbers $x,y,$ and $z$ satisfy \[\frac{\sqrt{x}+13}{y} = \frac{\sqrt{y}+29}{z} = \frac{\sqrt{z} + 46}{x} = 2\] and \[\frac{\sqrt{x} + \sqrt{y}+\sqrt{z}}{x+y+z} = \frac{6}{25}.\] Find the value of $x+y+z$.

Solution

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