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1955 AMC 12 Question 42

AMC12 · 1955 AMC 12

Question 42

If $a,$ $b,$ and $c$ are positive integers, the radicals $\sqrt{a+\dfrac bc}$ and $a\sqrt{\dfrac bc}$ are equal when and only when:
  1. $a=b=c=1$
  2. $a=b$ and $c=a=1$
  3. $c=\dfrac{b(a^2-1)}a$
  4. $a=b$ and $c$ is any value
  5. $a=b$ and $c=a-1$