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1964 AMC 12 Question 24

AMC12 · 1964 AMC 12

Question 24

Let $y=(x-a)^2+(x-b)^2,$ $a,$ $b$ constants. For what value of $x$ is $y$ a minimum?
  1. $\dfrac{a+b}{2}$
  2. $a+b$
  3. $\sqrt{ab}$
  4. $\sqrt{\dfrac{a^2+b^2}{2}}$
  5. $\dfrac{a+b}{2ab}$