The difference between the squares of two consecutive numbers is 31. Find the numbers.

Explanation

Let first number`=x`
The second number`=x+1`.
Given:
The difference between the squares of two consecutive numbers`=31`.
According to the question:
`(x+1)^2-x^2=31`
`x^2+2x+1-x^2=31`
`2x=31-1`
`2x=30`
`x=15`
`therefore` The first number`=15`
The second number`=15+1=16`
Hence, the numbers are `15, 16`.