Question

what two numbers multiplied together equal -16 but equal 15 when added?

Answer 1

x, y - the numbers

$xy=-16 \\ x+y=15 \\ \\ \hbox{solve the second equation for y:} \\ x+y=15 \\ y=15-x \\ \\ \hbox{substitute 15-x for y in the first equation:} \\ x(15-x)=-16 \\ 15x-x^2=-16 \\ -x^2+15x+16=0 \\ -x^2-x+16x+16=0 \\ -x(x+1)+16(x+1)=0 \\ (-x+16)(x+1)=0 \\ -x+16=0 \ \lor \ x+1=0 \\ x=16 \ \lor \ x=-1 \\ \\ y=15-x \\ y=15-16 \ \lor \ y=15-(-1) \\ y=-1 \ \lor \ y=16 \\ \\ (x,y)=(16,-1) \hbox{ or } (x,y)=(-1,16)$

The numbers are -1 and 16.

Answer 2

the possible combinations for 2 numbers multiplied together to = 16 are 16 and 1 8 and 2 4 and 4 -16 (1)= -16 16 + (-1) =15 hope this helps