Question

What two numbers multiplied together equal -8 and added together equal 6.  They have to be the same two numbers.

Answer 1

If the numbers are a and b, we have ab=-8 and a+b=6. We can replace b with 6-a in the first equation: a(6-a)=-8 so 6a-a^2=-8. Rearranging: a^2-6a-8=0 and completing the square: a^2-6a+9-17=0. Therefore (a-3)^2=17. Taking the square root of each side we have a-3=+sqrt(17) and a=3+sqrt(17) and b=6-(3+sqrt(17))=3-sqrt(17), which is the other alternative for a, so whichever way round the two numbers are 3+sqrt(17)=7.1231 and -1.1231 (approx). Add them together and we get 6; multiply them and we get -8.