What pair of square numbers gives a difference of 1100

Let us assume numbers are x and y.

Difference of the squares of x and y = 1100.

We can setup an equation:

x^2 - y^2 = 1100.

We can apply difference of the squares formula: a^2-b^2 = (a-b) (a+b).

Therefore,

x^2 - y^2 = 1100 would become (x-y) (x+y) = 1100.

Let us find all factors of 1100 square of those differences is 1100.

Let us take factors of 1100 as 110 and 10.

Sum should be 110 and difference should be 10.

So, we could setup two eqautions as

x+y=110

x-y=10

Adding equations, we get

2x = 120.

Dividing both sides by 2, we get

x=60.

Plugging x=60 in x+y=110, we get

60+y=110.

y=50.

Therefore, 60 and 50 pair of square numbers gives a difference of 1100.