IMO Shortlist 1995 problem A4
Find all of the positive real numbers like
such that :
1.)
2.)
Proposed to Gazeta Matematica in the 80s by VASILE CÎRTOAJE and then by Titu Andreescu to IMO 1995.
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Find all of the positive real numbers like $x,y,z,$ such that :
1.) $x + y + z = a + b + c$
2.) $4xyz = a^2x + b^2y + c^2z + abc$
Proposed to Gazeta Matematica in the 80s by VASILE CÎRTOAJE and then by Titu Andreescu to IMO 1995.
Source: Međunarodna matematička olimpijada, shortlist 1995
Školjka 
