Question

the product of two consecutive positive integers is 420. find the integer

Answer 1

Let take the integer as ‘’a’’ and its consecutive is ‘’a + 1’’

Formula: a * (a + 1) = a + a2

a * (a + 1) = a + a2 =  420

a2 + a - 420 = 0 --- > equation 1

Step 1: Factoring the equation1, we get the integer.

a2 + a - 420 = 0

a2 -20a + 21a - 420 = 0

a (a - 20) + 21 (a - 20) = 0

(a -20) (a + 21) = 0

Possibilities of ‘’a’’ value is

a = 20

a = -21

Answer 2

Let the one integer be x

second ineteger be x + 1

ATQ

x ( x + 1) = 420

x^2 + x = 420

x^2 + x - 420 = 0

x^2 + (21 - 20)x - 420 = 0

x^2 +21x - 20x - 420 = 0

x ( x + 21) - 20 ( x + 21) = 0

(x + 21) ( x - 20) = 0

The two numbers are positive so the integers are 20 and - 21