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Omni-MATH / If x, y, z are positive numbers satisfying

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

If xx, yy, zz are positive numbers satisfying x+yz=y+zx=z+xy=2.x+\frac{y}{z}=y+\frac{z}{x}=z+\frac{x}{y}=2. Find all the possible values of x+y+zx+y+z.
Plain-text mathematical notation (without MathML)
If x, y, z are positive numbers satisfying 
x+(y)/(z)=y+(z)/(x)=z+(x)/(y)=2.
Find all the possible values of x+y+z.
Original LaTeX notation
If $x$, $y$, $z$ are positive numbers satisfying 
\[x+\frac{y}{z}=y+\frac{z}{x}=z+\frac{x}{y}=2.\]
Find all the possible values of $x+y+z$.

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Source and history

task_id
700f97e3-c6cc-5155-9d51-3ce6ac751e7b
task_key
test--700f97e3-c6cc-5155-9d51-3ce6ac751e7b
task_revision_id
1
config / split
/ test

Official source

initial import