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If n is a positive integer, which of the...

If n is a positive integer, which of the following two will always be integers:
(I) `(sqrt(2)+1)^(2n)+(sqrt(2)-1)^(2n)`
(II) `(sqrt(2)+1)^(2n)-(sqrt(2)-1)^(2n)`
(III) `(sqrt(2)+1)^(2n+1)+(sqrt(2)-1)^(2n+1)`
(IV) `(sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)`

A

Only I and II

B

Only I and III

C

Only I and IV

D

Only II and III

Text Solution

Verified by Experts

The correct Answer is:
C
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