Find two consecutive odd integers such that the sum of their squares is 130
Let's assume that the first odd integer is x. Since it is odd, the next consecutive odd integer will be x + 2.
The sum of their squares is calculated as follows:
x^2 + (x + 2)^2 = 130
Expanding the equation:
x^2 + x^2 + 4x + 4 = 130
Combining like terms:
2x^2 + 4x + 4 = 130
Moving all terms to one side of the equation:
2x^2 + 4x - 126 = 0
Dividing by 2 to simplify:
x^2 + 2x - 63 = 0
Factoring the quadratic equation:
(x + 9)(x - 7) = 0
Setting each factor equal to zero:
x + 9 = 0 or x - 7 = 0
Solving each equation:
x = -9 or x = 7
Therefore, the two consecutive odd integers could be -9 and -7 or 7 and 9.