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Australian AMC 2019 - Senior Question 14

AMC AUSTRALIA · Australian AMC 2019 - Senior

Question 14

Which number exceeds its square by the greatest possible amount?
  1. $\frac12$
  2. $\frac23$
  3. $\frac14$
  4. $\frac34$
  5. $\frac{\sqrt2}2$