The sum of the squares of two consecutive natural numbers is 313. Find the numbers.


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Answer:

12 and 13

Step by Step Explanation:
  1. Let the numbers be x and x+1.
  2. x2 + (x+1)2 = 313
  3. 2x2 + 2x + 1 = 313
  4. 2x2 + 2x - 312 = 0
  5. x2 + x - 156 = 0
  6. x2 + 13x - 12x - 156 = 0
  7. x(x + 13) - 12(x + 13) = 0
  8. (x - 12) (x + 13) = 0
  9. x = 12 or -13. Since x cannot be negative, x = 12. Hence, numbers are 12 and 13.

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