Question 1180887


let two numbers  be {{{x}}} and {{{y}}}

if they differing by {{{48 }}} we have

{{{y=x+48}}}..........eq.1

Their product is

{{{P=xy }}}.......eq.2, substitute {{{x}}}

Since {{{y=x+48}}},

{{{P=(x+48)x}}}
{{{P=x^2+48x}}}

minimize the function by calculating {{{P}}}'{{{(x)}}}

{{{P}}}'{{{(x)=2x+48}}}

Setting it to {{{0}}}, we get

{{{0=2x+48}}}
{{{0=2(x+24)}}}

=>{{{x=-24}}}

then
 {{{y=-24+48}}}..........eq.1
{{{y=24}}}

so, your numbers are {{{24}}} and {{{-24}}}