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 inte

Question

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 inte

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

Monjur Alahi

8 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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

8 views Answered 2023-02-05 15:29