Hi Sarah,

I think the easiest way to do this is just to try some consecutive, odd positive integers.

1² + 3² = 10
3² + 5² = 34
5² + 7² = 74

However I expect you are to use algebra. So how do you express two consecutive odd positive integers algebraically? An odd number is one more than an even number so if n is any non-negative integer 2n + 1 is odd. The next number is 2n + 2 which is eve and the next number is 2n + 3 which is odd. Thus 2n + 1 and 2n + 3 are two consecutive odd positive integers. Hence you need to find n if

(2n + 1)² + (2n + 3)² = 74

Expand this expression to obtain a quadratic in n. Factor the quadratic and solve for n. You already know that 2n + 1 = 5 and 2n + 3 = 7 so that's a check on your work.

Penny