The sum of the squares of two positive, consecutive odd integers is 74. Find the integers.

Let the first odd integer = 2n - 1   and let the second = 2n + 1    so we have

(2n - 1)^2  +  (2n + 1)^2   = 74

4n^2  - 4n + 1  + 4n^2 + 4n + 1   =  74

8n^2 + 2  =74

8n^2  = 72     

n^2  = 9

n = 3

So....the two integers are  2(3) - 1   = 5   and  2(3) + 1  = 7