the difference of square #s?

Question

were doing are homework and we need help with this
if 21 = 5^2 - 2^2 and 11^2 - 10^2, how do you find the equation for numbers there are more than one way to square.
the #s that have more than one way r :

9, 15,16, 21, 24, and 25.
none of the eqations we come up with work for 21.thanx

Answer 1

How about 5² - 2² ?

Here's the thing to realize. The difference between two consecutive squares is always an odd number.

1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
25 - 16 = 9
36 - 25 = 11
49 - 36 = 13
64 - 49 = 15
...

For an even number, you can sometimes take half of it and find the odd numbers on either side. For example 24. Half would be 12. So take the two differences that make 11 and 13. That means 49 - 25 = 24.

In the case of 21, you can use 5 + 7 + 9... so use 25 - 4 = 21.

It's usually a little trial and error, and as you noted, there are often many ways to create the number.