Question

If p and n are integers such that p>n>0 and p^2-n^2=12, which of the following can be the value of p - n? I. 1 II. 2 III. 4

Answer 1

First rewrite `p^2-n^2=(p+n)(p-n)=12`

Explanation:

`12` can only be factorised in a few ways:
`12=12*1=6*2=4*3` which would be the values of `p+nandp-n` respectively.
The difference of these two factors is then `=2n`

This leaves only the `6*2` combination, as the other two would give a non-integer solution for `n`

Answer : `p-n=2`

Extra : `p=4andn=2`