Question

Fine two consecutive integers such that the square of the smaller is 10 more than the larger ?

Answer 1

This is not possible.

Explanation:

The difference between the squares of two consecutive integers is

`(n+1)^2-n^2=2n+1`

which is always odd. Thus, this can not be equal to 10 for any pair of consecutive integers.

Note that the square of the smaller integer being larger is not a problem, all that this would mean is that the numbers are negative!

Answer 2

This is not possible.

Explanation:

The difference between the squares of two consecutive integers is

`(n+1)^2-n^2=2n+1`

which is always odd. Thus, this can not be equal to 10 for any pair of consecutive integers.

Note that the square of the smaller integer being larger is not a problem, all that this would mean is that the numbers are negative!