Find three odd consecutive integers such that the sum of the squares of the first and second integers is equal to the square of the third integer plus 9

Question

 I need to answer this problem and provide what the three numbers are and if there is only one solution or multiple solutions.

Answer 1

Let the three consecutive odd integers be x, x+2 & x+4.

Your sentence (question) says x² + (x+2)²  = 9 + (x+4)² 

 

Can you solve this? BTW: check that the answer is indeed an ODD integer x and its two odd successors.

Answer 2

If you want to check answers, I get 2 solution sets:

 

{7, 9, 11} and {-3, -1, 1}.