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.
