Question

Find two consecutive numbers whose square differ by 31

Answer 1

First number = x
Consecutive number = x+1
"squares differ by 31" means to square both numbers and subtract them:
(x+1)^2 - (x)^2 = 31
x^2+2x+1 - x^2 = 31
2x+1 = 31
2x = 30
x = 15 (first number)
x+1 = 15+1 = 16 (consecutive number)