Question 1128066

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


{{{xy=-3}}} and assuming {{{y>x}}}, {{{y+x=-5}}}.
Two equations and two unknown variables.


{{{y=-5-x}}} from the second equation.
{{{x(-5-x)=-3}}} substituted into the first equation.
{{{-x^2-5x=-3}}}
{{{x^2+5x-3=0}}}..........cannot be factored completely, so use quadratic formula and you will get
{{{x = -5/2 - sqrt(37)/2}}} or {{{x = -5/2 + sqrt(37)/2}}} 

then, go to {{{y=-5-x}}} and find {{{y}}}

{{{y=-5-(-5/2 - sqrt(37)/2)}}}

{{{y=-5+5/2 + sqrt(37)/2}}}

{{{y=-10/2+5/2 + sqrt(37)/2}}}

{{{y=-5/2 + sqrt(37)/2}}} or  {{{y=-5/2 + sqrt(37)/2}}}


{{{highlight(exact)}}} solutions are: assuming {{{y>x}}}

{{{x = -5/2 - sqrt(37)/2}}}
{{{y=-5/2 + sqrt(37)/2}}} 

check:

{{{( -5/2 - sqrt(37)/2)(-5/2 + sqrt(37)/2)=-3}}}

{{{(( -5 - sqrt(37))(-5+ sqrt(37)))/4=-3}}}

{{{(( -5)^2 - (sqrt(37))^2)/4=-3}}}

{{{(25 - 37)/4=-3}}}

{{{ - 12/4=-3}}}

{{{ - 3=-3}}}


{{{( -5/2 - sqrt(37)/2)+(-5/2 + sqrt(37)/2)=-5}}}

{{{ -5/2 -cross( sqrt(37)/2)-5/2 + cross(sqrt(37)/2)=-5}}}

{{{-5/2 -5/2 =-5}}}

{{{ -10/2 =-5}}}

{{{ -5 =-5}}}