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.

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