Problems based on Numbers Test 4

Question : 27 of 40

Marks: +1, -0

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

Solution:

Let the two positive integers be x and y; then

x - y = 3

...(i)

x^2 + y^2 = 369

...(ii)
Now,

(x - y)^2 = x^2 + y^2 - 2xy

⇒ (3)^2 = 369 - 2xy

⇒ 2xy = 360

⇒ xy = 180

Again,

(x + y)^2 = (x - y)^2 + 4xy

= (3)^2 + 4 × 180 = 729

∴

x+y=√729=27

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