Consecutive Integers

Question

Find three consecutive integers such the product of the second integer and the third integer is 20.

Answer 1

let the first integer be x

3 consecutive integers would be x, x + 1, x + 2

(x + 1) (x + 2) = 20

x = -6 or x = 3

-6, -5, -4

3, 4, 5

the product of -5 and -4 is 20.

the product of 4 and 5 is also 20.

Answer 2

Let i = 1st integer i+1 = 2nd integer i+2 = 3rd integer

Product of 2nd and 3rd integer = 20

(i+1) (i+2) = 20

i^2 +3i + 2 = 20

i^2 +3i -18 = 0 Subtracting 20 from both sides of the equation.)

(i - 3) (i + 6) = 0 Factoring

i - 3 = 0 AND i + 6 = 0 If the product of two numbers is ZERO, then one or both are zero.

i = 3 AND i = -6 Adding 3 to both sides in i-3=0 and subtracting 6 from both sides in i+6+0.

ANSWERS: 3,4,5 AND -6,-5,-4

3,4,5 since i=3, i+1=4, and i+2=5

-6,-5,-4 since i = -6, i+1=-5, and i+2=-4

CHECKING:

Does the 2nd times the 3rd = 20?

(4)(5) = 20 YES

(-5)(-4) = 20 YES

Hope this was helpful Geraldine.