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Omni-MATH / Find all of the positive real numbers like x,y,z, such that :

Problem

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problem

Find all of the positive real numbers like x,y,z, x,y,z, such that : 1.) $ x \plus{} y \plus{} z \equal{} a \plus{} b \plus{} c$ 2.) $ 4xyz \equal{} a^2x \plus{} b^2y \plus{} c^2z \plus{} abc$ Proposed to Gazeta Matematica in the 80s by VASILE C?RTOAJE and then by Titu Andreescu to IMO 1995.
Plain-text mathematical notation (without MathML)
Find all of the positive real numbers like x,y,z, such that :

1.) $ x \plus{} y \plus{} z \equal{} a \plus{} b \plus{} c$

2.) $ 4xyz \equal{} a^2x \plus{} b^2y \plus{} c^2z \plus{} abc$

Proposed to Gazeta Matematica in the 80s by VASILE C?RTOAJE and then by Titu Andreescu to IMO 1995.
Original LaTeX notation
Find all of the positive real numbers like $ x,y,z,$ such that :

1.) $ x \plus{} y \plus{} z \equal{} a \plus{} b \plus{} c$

2.) $ 4xyz \equal{} a^2x \plus{} b^2y \plus{} c^2z \plus{} abc$

Proposed to Gazeta Matematica in the 80s by VASILE C?RTOAJE and then by Titu Andreescu to IMO 1995.

Discussion

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Source and history

task_id
594bd444-3213-5d62-a8b6-a1b52eded8b0
task_key
test--594bd444-3213-5d62-a8b6-a1b52eded8b0
task_revision_id
1
config / split
/ test

Official source

initial import