The number of positive integer values of n for which √n+1 + √n-1 is
rational, is equal to
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Thus we can say that √n+1 and √n−1 are perfect squares of positive integers. It contradicts the fact that two perfect squares differ by 3. 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.
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