The sum of the squares of two positive numbers is 100, and their difference of squares is 28. What is the sum of the numbers?
A
12
B
13
C
14
D
15
Correct Option:
C
Explanation
Let the numbers be x and y.
1. x² + y² = 100 and x² - y² = 28.
2. Adding the equations: 2x² = 128, so x² = 64 and x = 8.
3. Substituting: 64 + y² = 100, so y² = 36 and y = 6.
4. Sum of the numbers: x + y = 8 + 6 = 14.
