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Omni-MATH / Let x,y,z be real numbers satisfying (1)/(x)+y+z=x+(1)/(y)+z=x+y+(1)/(z)=3 The sum of all possible values of x+y+z can be written as (m)/(n), where m,n are positive integers and …

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problem

Let x,y,zx, y, z be real numbers satisfying 1x+y+z=x+1y+z=x+y+1z=3\frac{1}{x}+y+z=x+\frac{1}{y}+z=x+y+\frac{1}{z}=3 The sum of all possible values of x+y+zx+y+z can be written as mn\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
Let x,y,z be real numbers satisfying (1)/(x)+y+z=x+(1)/(y)+z=x+y+(1)/(z)=3 The sum of all possible values of x+y+z can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
Let $x, y, z$ be real numbers satisfying $$\frac{1}{x}+y+z=x+\frac{1}{y}+z=x+y+\frac{1}{z}=3$$ The sum of all possible values of $x+y+z$ can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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Source and history

task_id
bd172cf3-9b59-5628-999c-1a6275cde8c4
task_key
test--bd172cf3-9b59-5628-999c-1a6275cde8c4
task_revision_id
1
config / split
/ test

Official source

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