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Question 1058011: One integer is 3 less than another. The sum of their squares is 269 find the integers
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! Let x represent the first integer. The second integer is then represented by x - 3.
Since the sum of the squares is 269, you can write the following equation:
x^2 + (x - 3)^2 = 269
x^2 + x^2 - 6x + 9 = 269
2x^2 - 6x - 260 = 0
2(x^2 - 3x - 130) = 0
2(x - 13)(x + 10) = 0
x = 13, or x = -10
When x = 13, then the other number is 10.
When x = -10, then the other number is -13
Thus, there are two solutions:
1. 10 and 13
2. -10 and -13
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