# 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

1. 81
2. 33
3. 27
4. 25
Anurag Mishra Professor Asked on 12th October 2015 in

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, X2 + Y2 = 369        ………………………. (2)

From equation (1),
X – Y = 3
Square on both side,
(X – Y)2 = 32
X2 + Y2 – 2 X Y = 9
Put the value of X2 + Y2 = 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 = X2 + Y2 + 2 XY

Then, (X + Y)2 = X2 + Y2 + 2 XY
Put the value of X2 + Y2 = 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.

Anurag Mishra Professor Answered on 14th October 2015.