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1986 AMC 12 Question 30

AMC12 · 1986 AMC 12

Question 30

The number of real solutions $(x,y,z,w)$ of the simultaneous equations $$
\begin{aligned} 2y&=x+\frac{17}{x},\\ 2z&=y+\frac{17}{y},\\ 2w&=z+\frac{17}{z},\\ 2x&=w+\frac{17}{w}. \end{aligned}
$$ is
  1. $1$
  2. $2$
  3. $4$
  4. $8$
  5. $16$