Question :
The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares ?
Options :
- 106
- 196
- 53
- 68
correct answer : a)
Let positive numbers be a and b where a > b.
According to the question,
a – b = 56
ab = 5600
∴ (a – b)² = a² + b² – 2ab = 56²
a² + b² = 56² + 2 × 5600
= 3136 + 11200
= 14336