Question

The difference of two numbers is 3 and the difference of their square is69.Find the numbers.

Answer 1

Let the two numbers be x and y.
Difference of two numbers x-y=3 ------(i)
Difference of their squares x2 - y2=69
we have formula x2 - y2= (x+y(x-y)
Therefore, x2 - y2=69
(x+y)(x-y)=69
(x+y)(3)=69
x+y= 69/3
x+y= 23------(ii)
Now add equations (i) and (ii), we get
x+y=23
x-y=3
__________
2x =26
x=26/2
x=13
Now take equation (i) or equation (ii) to calculate y
x+y=23 ( From equation (ii)
13+y=23 ( Substitute x=13)
y=23-13
y=10
Therefore the two numbers are 13 and 10