IMO Shortlist 1984 problem 9


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2. travnja 2012.
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Let a, b, c be positive numbers with \sqrt a +\sqrt b +\sqrt c = \frac{\sqrt 3}{2}. Prove that the system of equations
\sqrt{y-a}+\sqrt{z-a}=1, \sqrt{z-b}+\sqrt{x-b}=1, \sqrt{x-c}+\sqrt{y-c}=1
has exactly one solution (x, y, z) in real numbers.
Izvor: Međunarodna matematička olimpijada, shortlist 1984