Question 685079

let's two positive numbers be {{{x}}} and {{{y}}}


The difference of two positive numbers is {{{9}}}: 

{{{x-y=9}}}........1

and their product is {{{220}}}:

{{{x*y=220}}}........2

solve the system:

{{{x-y=9}}}........1

{{{x*y=220}}}........2
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{{{x-y=9}}}........1....solve for {{{x}}}

{{{x=9+y}}}.......substitute in 2


{{{(9+y)*y=220}}}........2...solve for {{{y}}}

{{{9y+y^2=220}}}

{{{y^2+9y-220=0}}}.....use quadratic formula


{{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{y = (-9 +- sqrt( 9^2-4*1*(-220) ))/(2*1) }}} 

{{{y = (-9 +- sqrt( 81+880 ))/2 }}} 

{{{y = (-9 +- sqrt( 961 ))/2 }}}

{{{y = (-9 +- 31)/2 }}}

find only positive solution since numbers we are looking for are positive


{{{y = (-9 + 31)/2 }}}

{{{y = 22/2 }}}

{{{highlight(y = 11) }}}


now find {{{x}}}


{{{x=9+y}}}

{{{x=9+11}}}

{{{highlight(x=20)}}}