This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2016 CMIMC, 3
Tags: algebra , system of equations , yuh.
Suppose $x$ and $y$ are real numbers which satisfy the system of equations \[x^2-3y^2=\frac{17}x\qquad\text{and}\qquad 3x^2-y^2=\frac{23}y.\] Then $x^2+y^2$ can be written in the form $\sqrt[m]{n}$, where $m$ and $n$ are positive integers and $m$ is as small as possible. Find $m+n$.

2011 AIME Problems, 15
Tags: vieta , quadratic , yuh. , polynomial , algebra
For some integer $m$, the polynomial $x^3-2011x+m$ has the three integer roots $a$, $b$, and $c$. Find $|a|+|b|+|c|$.