The difference between two positive numbers is 3. If the

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The difference between two positive numbers is 3. If the sum of their squares is 369, then the sum of the numbers is :

1. 81
2. 33
3. 27
4. 25

Correct Option: C

Let the number be x and y and x > y.
x – y = 3 ...(i)
x² + y² = 369 ....(ii)
From equation (i)
x – y = 3
⇒ (x – y)² = 3²
⇒ x² + y² – 2xy = 9
⇒ = (x² + y²) – 9
= 369 – 9 = 360
From equation (ii)
Now,(x² + y²) = x² + y² + 2xy
= 369 + 360 = 729
∴ x + y = √729 = 27
∴ Required sum = 27