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1974 AMC 12 Question 30

AMC12 · 1974 AMC 12

Question 30

A line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. If $R$ is the ratio of the lesser part to the greater part, then the value of $$
R^{\left[R^{\left(R^2+R^{-1}\right)}+R^{-1}\right]}+R^{-1}
$$ is
  1. $2$
  2. $2R$
  3. $R^{-1}$
  4. $2+R^{-1}$
  5. $2+R$