Find all the positive integers ' n ' for which \sqrt{n-1}+\sqrt{n+1} is rational.
ans---------------> no positive integers
29The series of the pefect squares of the integers goes like this
1,4,9,16,25,36,49...
so u can observe that none of the terms differ by 2..
so the above mentioned equation has no rational term..
well this is wat i thot...maybe experts can provide a better proof for this..
11I did not get u Uttara....
\frac{p}{q}=\frac{1}{\sqrt{n-1}+\sqrt{n+1}}
From which we have
p^2(2n-2\sqrt{n^2-1})=q^2 - thus n2-1 must be a perfect square - which gives n=1, which is obviously not possible.
