The sum of the squares of two consecutive odd positive intergers is 130. Find the integers.

Question

(Factoring word problem with GCF) The sum of the squares of two consecutive odd positive integers is 130. Find the integers.

Answer 1

x² + (x + 2)² = 130

 

x² + x² + 4x + 4 = 130

 

2x² + 4x + 4 = 130

 

divide above by 2:

 

x² + 2x + 2 = 65

 

x² + 2x - 63 = 0

 

(x + 9)(x - 7) = 0

 

x = -9, or 7

 

since we need positive numbers, it's  7, 9