Question

The difference of two number is 3 and the difference of their square is 69.find the numbers

Answer 1

Let the numbers be x & y.

Given that the difference between two numbers = 3.

x - y = 3

x = y + 3   ------------ (1).


Given that the difference of their square = 69

x^2 - y^2 = 69

(y + 3)^2 - y^2 = 69

We know that (a+b)^2 = a^2+b^2+2ab

y^2 + 9 + 6y - y^2 = 69

6y = 69 - 9

6y = 60

y = 10.


Now substitute y = 3 in (1), we get

x = y + 3

x = 10 + 3

x = 13.


Therefore the numbers are 13 and 10.


Verification:

13 - 10 = 3

13^2 - 10^2 = 169 - 100

                   = 69.


Hope this helps!

Answer 2

Let the two numbers be x and y
Therefore,
x - y = 3
and, x^2 - y^2 = 69
= (x -y)(x + y)
Therefore,
3(x +y) = 69
x + y = 69/3
x + y = 23
Therefore,
x - y = 3
- (x + y = 23)
-2y = -20
y = 10
x - 10 = 3
x = 13