Question

Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.

Answer 1

Let the two numbers be x and y. Then, as per the question,

x² + y² = 656 ...... (i) 

and x - y = 4 

⇒  x = 4 + y ........ (ii) 

Putitng 2nd equation in first, we get: 

(y+4 )² + y² = 656,

⇒ 2y² + 8y - 640 = 0 

⇒ y² + 4y - 320 = 0 

⇒ y² + 20y -16y- 320 = 0 

⇒ y(y+ 20) - 16 (y+20) = 0 

⇒ (y-16 ) (y+ 20) = 0 

y can't be negative, hence y= 16 

x= y+4 = 20 

Hence numbers are 16 and 20.