Question

How many pairs of natural numbers are there so that the difference of their squares is 60?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Let x and y be two natural numbers  

Given    x^2 -y^2 = 60

  [x+y] [x-y] = 60

suppose  x +y  and  x - y  are odd numbers  then  the product can not be 60

suppose  one factor  is odd and  one factor is  even  

               x + y  + x -y is odd

               2 x  is odd    it is also impossible

so two factors  x- y and x + y are even

 so 60 = 2 x 30 =6 x 10   are chances  to both even factors

case 1    x+ y =30 and x - y = 2   then x=16 ,y =14

case 2    x+y =10 and  x - y =6    then  x = 8 , y = 2