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HMMT — a=(b+c)/(x-2) b=(c+a)/(y-2) c=(a+b)/(z-2) Complex

1925SpecialistComplex NumbersSystems Of EquationsAlgebra

13th Annual Harvard-MIT Mathematics Tournament

Let $a$, $b$, $c$, $x$, $y$, and $z$ be complex numbers such that $$ a = \frac{b+c}{x-2}, \quad b = \frac{c+a}{y-2}, \quad c = \frac{a+b}{z-2}. $$ If $xy + yz + zx = 67$ and $x + y + z = 2010$, find the value of $xyz$.
0 students attempted0% solvedRating 1925

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