SOLUTION: two positive number differ by 7 and the sum of their square is 169. find the numbers

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Question 471543: two positive number differ by 7 and the sum of their square is 169. find the numbers
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
5,12,13 works (simply recall the 5-12-13 right triangle and that 5^2 + 12^2 = 13^2).

To solve it algebraically, let x and x+7 be the numbers, with x^2 + (x+7)^2 = 169. Expand, and you will obtain a quadratic equation in terms of x. Either way, you will get 5 and 12 as the numbers.