the difference between first two perfect squares that ends up with 9

Question

the difference between first two perfect squares that ends up with 9

Answer 1

Assuming that the question is "Find the earliest two perfect squares that have a difference ending with the digit 9:"

 

A perfect square is a number that can be expressed as the product of two equal integers.

The list of perfect squares:

   0,  1,   4,    9,   16,   25,   36,   49,  ...

 

9 - 0 = 9

Answer 2

Let's try to set this up.

 

Let x and y be the two consecutive numbers you are squaring.

 

x+1 = y

 

The difference between their squares is 9

y² - x² = 9

 

Using substitution

(x+1)² - x² = 9

 

expanding

x² + 2x +1 - x² = 9

2x + 1 = 9

2x = 8

x = 4

 

Now let's double check

if x = 4, then y = 5

x² = 16

y² = 25

25-16=9