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If n is a positive integer, then (sqrt(3...

If n is a positive integer, then `(sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n)` is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

A

an irrational number

B

an odd positive integer

C

an even positive integer

D

a rational number other than positiveintegers

Text Solution

Verified by Experts

The correct Answer is:
A
`(3sqrt(3) + 1)^(2n)- (sqrt(3) - 1)^(2n)`
`=2[.^(2n)C_(1)(sqrt(3))^(2n-1)+.^(2n)C_(3)(sqrt(3))^(2n-3)+.^(2n)C_(5)(sqrt(3))^(2n-5) + "….."]`
= an irrational number
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