The sum of the squares of two positive numbers is 100 and

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The sum of the squares of two positive numbers is 100 and difference of their squares is 28. Find the sum of the numbers :

1. 12
2. 13
3. 14
4. 15

Correct Option: C

According to question
x² + y² = 100 ...(i)
x² − y² = 28 ...(ii)
Adding both the equations
x² + y²
x² − y²
-----------
2x²    128
⇒ x² = 64    ∴ x = 8
From the equation (i)
y² = 100 − 64    ∴ y = 6
So, x + y = 8 + 6 = 14