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1959 AMC 12 Question 35

AMC12 · 1959 AMC 12

Question 35

The symbol $\ge$ means “greater than or equal to”; the symbol $\le$ means “less than or equal to.” In the equation $(x-m)^2-(x-n)^2=(m-n)^2,$ $m$ is a fixed positive number, and $n$ is a fixed negative number. The set of values $x$ satisfying the equation is:
  1. $x\ge0$
  2. $x\le n$
  3. $x=0$
  4. the set of all real numbers
  5. none of these