Question

The product of two consecutive integers is equal to 14 more than 4 times the sum. This can be simplified to x²-7x-18=0. What are the two integers?

Answer 1

-1 and -2, or 9 and 10

Explanation:

If x is the smaller integer:

x (x + 1) = 14 + 4 (x + x + 1)

x² + x = 14 + 4 (2x + 1)

x² + x = 14 + 8x + 4

x² − 7x − 18 = 0

Factor using AC method:

(x − 9) (x + 2) = 0

x = -2 or 9

x is the smaller integer, so the larger integers are -1 and 10. Check each pair of solutions.

-1 and -2:

(-2) (-1) = 14 + 4 (-2 + -1)

2 = 14 + 4 (-3)

2 = 2

9 and 10:

(9) (10) = 14 + 4 (9 + 10)

90 = 14 + 4 (19)

90 = 90

Both solutions work.