Question

Show that there is no positive integer n for which
✓n-1 + ✓n+1 is rational​

Answer 1

Answer:

(√n−1+√n+1)+(√n+1−√n−1)=pq+2qp⇒2√n+1=p2+2q2pq. (n+1) is a perfect square of positive integers. ... Thus there is no positive integer n for which √n−1+√n+1 is rational. Note: It is important to consider the expression equal to p/q, where p and q are integers and q≠0