Question

What is two numbers that multiply to 24 but add to 25?

Answer 1

x, y - the numbers


`xy=24 \\ x+y=25 \\ \\ \hbox{solve the second equation for y:} \\ x+y=25 \\ y=25-x \\ \\ \hbox{substitute 25-x for y in the first equation:} \\ x(25-x)=24 \\ 25x-x^2=24 \\ -x^2+25x-24=0 \\ -x^2+24x+x-24=0 \\ -x(x-24)+1(x-24)=0 \\ (-x+1)(x-24)=0 \\ -x+1=0 \ \lor \ x-24=0 \\ x=1 \ \lor \ x=24 \\ \\ y=25-x \\ y=25-1 \ \lor \ y=25-24 \\ y=24 \ \lor \ y=1`

The numbers are 1 and 24.