The product of two consecutive integers is 156. What are the two integers?

Question

The product of two consecutive integers is 156. What are the two integers?

Answer 1

let x and x+1 be the integers

x(x+1)=156

x^2+x=156

x^2+x-156=0

156=2*2*3*13

(2*2*3)*13=12*13 and 12*13=156

factor

(x+13)(x-12)=156

x-12=0

x=12 and x+1=13

12 and 13 are the integers

x+13=0

x=-13

x+1=-12

-12 and -13 is also a solution

using arithmetic...

√156=12.48999

truncate the number to get 12 and then 13 and then -12 and -13

Answer 2

Hi Harry, let x represent the first integer. Then, x + 1 will represent the second integer.

 

Equation to solve:

 

x * (x + 1) = 156

 

x² + x = 156

 

x² + x - 156 = 0

 

Look at the factors of 156 to find values that when multiplied equal 156 and when added will equal 1.

 

Answer:

 

(x - 12) * (x + 13) = 0

 

Solve for x:

 

x - 12 = 0

 

x = 12

 

And

 

x + 13 = 0

 

x = -13

 

Answer:

 

When x = 12, x + 1 = 13.

 

When x = -13, x + 1 = -12

 

Questions?