Question

The difference of 2 squared numbers equals 53, what are the numbers​

Answer 1

Answer:

  27, 26

Step-by-step explanation:

  27^2 -26^2 = 729 -676 = 53

If the numbers are integers, they must differ by an odd number. For some odd number k, we will have ...

  (x +k)^2 -x^2 = 53

  2xk +k^2 = 53

  x = (53 -k^2)/(2k)

  x = 53/(2k) -k/2

The second term is an odd multiple of 1/2. The first term will be an odd multiple of 1/2 only for k=1. For k = 1, we have ...

  x = (53 -1)/2 = 26

The two numbers are 26 and 27.