IMO Shortlist 1978 problem 16


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2. travnja 2012.
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Determine all the triples (a, b, c) of positive real numbers such that the system
ax + by -cz = 0, a \sqrt{1-x^2}+b \sqrt{1-y^2}-c \sqrt{1-z^2}=0,
is compatible in the set of real numbers, and then find all its real solutions.
Izvor: Međunarodna matematička olimpijada, shortlist 1978