Let the first odd integer be x, so the other consecutive odd integer is x + 2. So we have:
x^2 + (x + 2)^2 = 74
x^2 + x^2 + 4x + 4 = 74
2x^2 + 4x + 4 - 74 = 74 - 74
2x^2 + 4x - 70 = 0 divide by 2 to both sides
x^2 + 2x - 35 = 0
(x + 7)(x - 5) = 0
x + 7 = 0 or x - 5 = 0
x + 7 - 7 = 0 -7 or x - 5 + 5 = 0 + 5
x = -7 or x = 5
Thus, the first odd integer would be -7 or 5, and the second consecutive odd integer would be -5 (-7 + 2) or 7 (5 + 2).
Check:
find the two consecutive odd integers with a sum of 152
112+92 is 202.
3 and 5
The sum of two consecutive odd integers is an even number. There is no possible answer to this question.
The integers are 11, 13 and 15.
The two consecutive negative odd integers having 74 as the sum of their squares are -5 and -7.
find the two consecutive odd integers with a sum of 152
112+92 is 202.
If you have two consecutive integers then one of them must be odd and the other must be even. The square of an odd integer must be odd, the square of an even integer must be even. The sum of an odd number and an even number must be odd. Thus, the sum of squares of any two consecutive numbers must be odd. Therefore, the question has no valid answer.
9 and 11 92 = 81 112 = 121 81+121 = 202
3 and 5
The sum of two consecutive odd integers is an even number. There is no possible answer to this question.
The four consecutive odd integers are 43 + 45 + 47 + 49 = 184
They are 2n+2
72 - 52 = 49 - 25 = 24
There is a set of two consecutive integers that have a sum of 123; one odd and one even. They are 61 and 62.
The integers are 13 and 15.