Answer:
Answers: 9 and 7
Explanation:
Givens
The first odd number is n - 1 where n is even but taking one away makes it odd.
The second odd number is n+1 some condition as above except you are adding 1.
Equation
Sum of the odd number is (n - 1 + n + 1)
Their squares summed = (n + 1)^2 + (n - 1)^2
(n + 1 + n - 1)^2 - (n +1)^2 + (n - 1)^2 = 126
Solution
(2n)^2 - (n^2 + 2n + 1 + n^2 - 2n + 1) = 126 Collect like terms. Expand.
4n^2 - ( 2n^2 + 2) = 126 Remove the brackets
4n^2 - 2n^2 - 2 = 126 Collect like terms on the left.
2n^2 - 2 = 126 Add 2
2n^2 = 126 + 2 Combine
2n^2 = 128 Divide by 2
n^2 = 64 Take the square root
sqrt(n^2) = sqrt(64)
n = 8
Answer
n + 1 = 9
n - 1 = 7
Check
- (9 + 7)^2 = 16^2 = 256
- 9^2 + 7^2 = 81 + 49 = 130
- Difference = 256 - 130 = 126
Remark
What a really interesting problem. Thanks for posting.