Answer
Numbers are 210 and 210
Work Step by Step
Two numbers whose sum is 420, product is as large as possible
Let the numbers be represented by $x$ and $y$, and let the product be $z$
$x+y=420$
$xy = z$
$x+y-y=420-y$
$x=420-y$
$xy=z$
$(420-y)y=z$
$420y-y^2=z$
$-y^2+420y=z$
$a=-1$, $b=420$
$x=-b/2a$
$x=-420/2*-1$
$x=-420/-2$
$x=210$
$y=210$
$x+y=420$
$x+210=420$
$x+210-210=420-210$
$x=210$
