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How can we find all of the positive real numbers like $x$,$y$,$z$, such that :

1.) $x + y + z = a + b + c$(here $a$,$b$ and $c>0)$ and

2.) $4xyz = a^2x + b^2y + c^2z + abc$ ?(Both the conditions are simultaneously true)

Source: International Mathematics Olympiad 1995 Shortlist.

Edit: I received this problem from someone and the way it is stated, it is not quite right.I have included the condition $a$,$b$ and $c$ are also positive.I apologize for the error.(It got corrected thanks to user Phira and Puresky)

Thanks.

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    I did **not** say that you should not ask questions related to contests. My critique is equally true for any kind of math question. If you search for$a$"slicker, better" solution than the "conventional" one, but keep it secret, then your question is badly written. This has nothing whatsoever to do with contests. It is possible to describe a solution method without giving all the details.2011-11-13

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http://ohkawa.cc.it-hiroshima.ac.jp/AoPS.pdf/problem%20from%20the%20book.pdf

See page 30. There is a solution.

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    Since, the moderators haven't objected to this link, I am accepting the solution.Thanks.2011-11-13