The sum of square of two positive numbers is 208. If square of the larger number is 18 times the smaller number, find the numbers.


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Answer:

12 and 8

Step by Step Explanation:
  1. Let smaller number be x. Therefore square of larger number = 18x.
  2. x2 + 18x = 208
  3. x2 + 18x - 208 = 0
  4. x2 + 26x - 8x - 208 = 0
  5. x (x + 26) - 8 (x + 26) = 0
  6. (x + 26) (x - 8) = 0
  7. x = 8 or -26. Since numbers are positive, smaller number x = 8.
  8. Larger number = √(18 x 8) = 12

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