A) an irrational number
B) an odd positive integer
C) an even positive integer
D) a rational number other than positive integers
Correct Answer: A
Solution :
\[{{(\sqrt{3}+1)}^{2n}}-{{(\sqrt{3}-1)}^{2n}}\] \[=2{{[}^{2n}}{{C}_{1}}{{(\sqrt{3})}^{2n-1}}{{+}^{2n}}{{C}_{3}}{{(\sqrt{3})}^{2n-3}}{{+}^{2n}}{{C}_{5}}{{(\sqrt{3})}^{2n-5}}+...]\] = which is an irrational number
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