# The Sum of The Numbers is :

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

- 81
- 33
- 27
- 25

**Answer: (3) 27**

**Explanation:- **Let the two positive numbers be X & Y.

The difference between two positive numbers is 3.

Then, X – Y = 3 ………………………. (1)

If the sum of their squares is 369.

Then, X^{2} + Y^{2} = 369 ………………………. (2)

From equation (1),

X – Y = 3

Square on both side,

(X – Y)^{2} = 3^{2}

X^{2} + Y^{2} – 2 X Y = 9

Put the value of X^{2} + Y^{2} = 369 (From equation 2)

Then, 369 – 2 XY = 9

– 2XY = 9 – 369

– 2 XY = – 360

XY = 360/2

XY = 180 ……………………………(3)

Formula-

(X + Y)^{2} = X^{2} + Y^{2} + 2 XY

Then, (X + Y)^{2} = X^{2} + Y^{2} + 2 XY

Put the value of X^{2} + Y^{2} = 369 and XY = 180 [From equation (2) & (3)]

(X + Y)^{2} = 369 +2 x 180

(X + Y)^{2} = 369 + 360

(X + Y)^{2} = 729

Square root on both side,

Then, X + Y = 27

Then, the sum of the number is 27.

Hence, the answer is (3) 27.