Question 1205514

let the larger number be {{{x}}}

if the larger of two positive numbers is {{{5}}} more than the smaller number {{{y}}}, we have

{{{x=y+5}}}...eq.1

If their product is {{{84}}}, we have

{{{x*y=84}}}...eq.2


substitute {{{x}}} from eq.1


{{{(y+5)*y=84}}}...eq.2, solve for {{{y}}}

{{{y^2+5y=84}}}

{{{y^2+5y-84=0}}}....factor

{{{y^2+12y-7y-84=0}}}

{{{(y^2-7y)+(12y-84)=0}}}

{{{y(y-7)+12(y-7)=0}}}

{{{(y - 7) (y + 12) = 0}}}


solutions:

{{{y =7}}} or {{{y =-12}}} 

go to eq.1

{{{x=y+5}}}...eq.1, substitute {{{y}}} 

{{{x=7+5}}}
{{{x=12}}}
or
{{{x=-12+5}}}
{{{x=-7}}}


answer:

 the numbers are:

{{{12}}} and {{{7}}}

or
{{{-7}}} and {{{-12}}}