Question

Show that there is no positive integer n for which underoot n-1 + underoot n+1 is rational.

Answer 1

if the √n+1 + √n+1 is rational no.

= √n+1 + √n+1 = -b/a. ( a and b is

co-prime integer)

= 2√n = -b/a - 1 - 1

= 2√n = -b/a - 2

= 2√n = (-b - 2a)/a

= √n = (-b - 2a)/2a

: this contradicts has assumption it is wrong because the √n is equals to rational are given so (-b - 2a)/2a is in the use of positive integer so

:we conclude that there is positive integer of √n