Answer:
{4, 13}
Step-by-step explanation:
Represent the integers by I and J. Then I + J = -17 and I*J = 52.
Let's solve this system using substitution. Solve the first equation for I as follows:
I + J = -17 becomes I = -J - 17
Substitute -J -17 for I in the second equation:
(-J - 17)*J = 52
Performing the indicated multiplication, we get:
-J^2 - 17J - 52 = 0
Let's solve this using the quadratic formula. The quadratic coefficients here are {-1, -17, -52}, and so the discriminant, b^2 - 4ac, is
(-17)^2 - 4(-1)(-52), or 289 - 208, or 81. This result is positive, so we know that the quadratic equation has two real, unequal roots. They are:
17 ± √81 17 ± 9
J = --------------- = ---------------
2(-1) -2
Evaluating this last result, we get J = (17 + 9)/2, or J = 13, and
J = (17 - 9)/2 = 8/2, or J = 4
