The sum of the squares of two positive consecutive odd integers is 34. What are the integers?

Step-by-step explanation:

So we can set up this problem like so:

x^2 + (x+2) ^2 = 34

You add two to the second x value because assuming the first x is odd you have to add 2 to get to the next odd integer

So:

x^2 + x^2 + 4x + 4 = 34

2x^2 + 4x + 4 = 34

2x^2 + 4x - 30 = 0

Factor this using the box method to get

x = - 3 or x = 5

Since it has to be positive we have x = 5

then add 2 to 5 to get the next answer - --> y = 7