Question

. Show that there is no positive integer n
for which under root n+1+ under root n+1 is rational.​

Answer 1

explanation:

let us assume that $\sqrt{n+1$ + $\sqrt{n-1}$ is rational

then it is = p/q where p and q are co-primes

on squaring both sides we get ;

2*n + 2*$\sqrt{n^{2}-1 }$=   $\frac{p^{2} }{q^{2} }$

on simplifying the above equation we get ;

$\sqrt{n^{2}-1 }$ =$\frac{p^{2}-2q^{2}n }{2q^{2} }$

hence $\sqrt{n^{2}-1 }$ is rational...

but two rational numbers differ at least by 3

hence assumption is wrong...

therefore $\sqrt{n+1}+\sqrt{n-1}$ is irrational

hence there is no real values of n such that the required equation is rational

pls mark as brainiliest

Answer 2

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