Question

a and b are consecutive, positive integers such that a^2−b^2>22. What is the minimum possible value of a+b?

Answer 1

since a and b are consective integers we could say that
a = b+1
then let the difference be
(b+1)^2 - b^2 > 22
b^2 + 2b + 1 - b^2 > 22
2b > 21
b > 10.5
so b has to be 11
a = 12
So a+b = 23

check: 12^2 - 11^2 = 144-121 = 23 which is > 22
try another value:
13^2-12^2 = 25
11^2-10^2 = 21