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Set of numbers satisfying equation

Source: 1959 AHSME Problem 35

August 14, 2013
AMC

Problem Statement

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(x-m)^2-(x-n)^2=(m-n)^2; m is a fixed positive number, and nn is a fixed negative number. The set of values xx satisfying the equation is: <spanclass=′latex−bold′>(A)</span> x≥0<spanclass=′latex−bold′>(B)</span> x≤n<spanclass=′latex−bold′>(C)</span> x=0<spanclass=′latex−bold′>(D)</span> the set of all real numbers<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ x\ge 0 \qquad<span class='latex-bold'>(B)</span>\ x\le n\qquad<span class='latex-bold'>(C)</span>\ x=0\qquad<span class='latex-bold'>(D)</span>\ \text{the set of all real numbers}\qquad<span class='latex-bold'>(E)</span>\ \text{none of these}
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