Question

the difference of two numbers is 3 and the difference of their squares is 27 find the numbers

Answer 1

Let the two numbers be x and y.
Therefore,
x - y = 3 
x^2 -y^2 = 27
[ x + y ] [ x - y ] = 27
but x - y = 3
so 
[ x + y ] * 3 = 27
therefore,
x + y = 9

now by solving the two equations by elimination method,
x+ y = 9 and x - y = 3

x = 6 and y = 3

therefore the two numbers are 6 and 3.

Answer 2

May this will help you