Answer:
The two consecutive odd integers are -17 , -15 OR 15 , 17
Step-by-step explanation:
* Lets explain how to solve the problem
- The difference between each two consecutive odd integers is 2
- Assume that the first odd number is x, then the second odd integers
is x + 2
∴ The two consecutive odd integers are x and x + 2
- The sum of their squares is 514
∵ The square of x is x²
∵ the square of x + 2 is (x + 2)²
∵ the sum of their squares is 514
∴ x² + (x + 2)² = 514
- Lets simplify it and solve it
∵ x² + (x + 2)² = 514
- Solve the bract of power 2
∵ (x + 2)² = (x)(x) + 2(x)(2) + (2)(2)
∴ (x + 2)² = x² + 4x + 4
∴ x² + x² + 4x + 4 = 514
- Add the like terms
∴ 2x² + 4x + 4 = 514
- Subtract 514 from both sides
∴ 2x² + 4x - 510 = 0
- All the terms have 2 common factor, then divide both sides by 2
∴ x² + 2x - 255 = 0
- Factorize the quadratic into two factors
∴ (x + 17)(x - 15) = 0
- Equate each factor by 0
∴ x + 17 = 0 OR x - 15 = 0
∵ x + 17 = 0
- Subtract 17 from both sides
∴ x = -17
- OR
∵ x - 15 = 0
- Add 15 to both sides
∴ x = 15
∵ x represents the first odd number
∴ x + 2 = -17 + 2 = -15 OR x + 2 = 15 + 2 = 17
∴ The two consecutive odd integers are -17 , -15 OR 15 , 17
