1960 AMC 12 Question 22
AMC12 · 1960 AMC 12
The equality $(x+m)^2-(x+n)^2=(m-n)^2,$ where $m$ and $n$ are unequal non-zero constants, is satisfied by $x=am+bn$ where:
$a=0,$ $b$ has a unique non-zero value
$a=0,$ $b$ has two non-zero values
$b=0,$ $a$ has a unique non-zero value
$b=0,$ $a$ has two non-zero values
$a$ and $b$ each have a unique non-zero value