Answer:
-8 and 7
Step-by-step explanation:
Let the integers be x and y.
Then, we have two conditions:
(1) x + y = -1
(2) xy = -56
(3) y = -x -1 Subtracted y from each side of (1)
(4) x(-x -1) = -56 Substituted (3) into (2)
-x² - x = -56 Distributed x
x²+ x = 56 Multiplied each side by -1
x²+ x - 56 = 0 Subtracted 56 each side
(x+8)(x - 7) = 1 Factored the quadratic
x + 8 = 0 x - 7 = 0
x = -8
For x = -8,
-8 + y = -1
y = 7
For x = 7,
7 + y = -1
y = -8
The pair of integers is -8 and 7.
