Question

Find two consecutive counting numbers whose squares differ by 35.

Answer 1

the numbers are n and n+1
the difference is 35
(n+1)^2-n^2=35
expand
n^2+2n+1-n^2=35
combine like terms
2n+1=35
minus 1 from oth sides
2n=34
divide by 2
n=17

the other number is 1 more

17 and 18
check
17^2=289
18^2=324
324-289=35


17 and 18

Answer 2

`(n+1)^2-n^2=35\\ n^2+2n+1-n^2=35\\ 2n=34\\ n=17\\ n+1=18`

17 and 18