Question

Show that there is no positive integer n which root of n -1 + root of n+1 is rational.

Answer 1

√n-1 + √n+1 can only be rational if both are whole squares.
the series of whole squares is like this:
1,4,9,16...
n-1 and n+1 have a difference of 2, but the least difference in whole squares is 3 so its impossible