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If n is a positive integer which of the following will always be integers?

\text { I. }(\sqrt{2}+1)^{2 n}+(\sqrt{2}-1)^{2 n} \quad \text { II. }(\sqrt{2}+1)^{2 n}-(\sqrt{2}-1)^{2 n}

\text { III. }(\sqrt{2}+1)^{2 n+1}+(\sqrt{2}-1)^{2 n+1} \text { IV. }(\sqrt{2}+1)^{2 n+1}-(\sqrt{2}-1)^{2 n+1}

Option: 1

only I and III


Option: 2

only I and II

 


Option: 3

only I and IV


Option: 4

only II and III


Answers (1)

best_answer

In I and IV only even powers of \sqrt{2} occurs whereas in II and III only odd powers of \sqrt{2} occurs.

Hence (C) is the correct answer.

 

Posted by

shivangi.bhatnagar

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