## anonymous 5 years ago Find all positive integers n for which $\sqrt (n-1)+\sqrt (n+1)$ is rational

1. anonymous

hmm i think, there is no positive integer n which works...

2. anonymous

Well, that may be true, but how can I prove that?

3. anonymous

well i was never good in proving things but to get a rational solution sqr.(n-1) and sqr. (n+1) have to be rational, otherwise a rational number would be added to a irrational number. so you have to find solutions for sqr. (n-1) which fit into the given conditions like: M = {2; 5; 10...} and the answers for sqr. (n+1): N= {0, 3, 8...} both sets have no common numbers and will never have one so there is no n which solves the task. that is no proof, but maybe it will help you or show that i got it wrong xD