Question 366524
1.{{{A+B=-15}}}
2.{{{A*B=225}}}
From eq. 2,
{{{A=225/B}}}
Substitute into eq. 1,
{{{225/B+B=-15}}}
{{{B^2+225=-15B}}}
{{{B^2+15B+225=0}}}
Use the quadratic formula,
{{{B = (-15 +- sqrt( 15^2-4*1*225 ))/(2*1) }}}
 {{{B = (-15 +- sqrt( 225-900 ))/(2) }}}
 {{{B = (-15 +- sqrt( -675 ))/(2) }}}
 {{{B = (-15 +- 15sqrt( 3)i)/(2) }}}
{{{B = (15/2)(-1 +-sqrt( 3)i) }}}
Then using eq. 1,
{{{A=(15/2)(-1 +-sqrt( 3)i) }}}
So the two numbers are,
{{{highlight(A=(15/2)(-1+sqrt(3)i))}}}
{{{highlight(B=(15/2)(-1-sqrt(3)i))}}}
and
{{{highlight_green(A=(15/2)(-1-sqrt(3)i))}}}
{{{highlight_green(B=(15/2)(-1+sqrt(3)i))}}}