Answer
-50 and 50
Work Step by Step
Two numbers whose difference is 100, product is as small as possible
Let the numbers be represented by $x$ and $y$, and let the product be $z$
$x-y=100$
$xy = z$
$x-y+y=100+y$
$x=100+y$
$xy=z$
$(100+y)y=z$
$100y+y^2=z$
$y^2+100y=z$
$a=1$, $b=100$
$x=-b/2a$
$x=-100/2*1$
$x=-100/2$
$x=-50$
$y=-50$
$x=-50$
$x-y=100$
$x-(-50)=100$
$x+50=100$
$x+50-50=100-50$
$x=50$
