2016 · Q9
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference between the two numbers?
Elementary MathematicsNumber System
- A2
- B3
- C4
- D6
Explanation
Let the numbers be x>y with x²+y² = 208 and x² = 18y. Substituting gives 18y+y² = 208, i.e. y²+18y−208 = 0, whose positive root is y = (−18+34)/2 = 8. Then x² = 144, so x = 12, and the difference is 12−8 = 4 (option C).