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  • If n is a positive integer, then <img alt="\left ( \sqrt{3} +1\right )^{2n}-\left ( \sqrt{3}-1 \right )^{2n}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cdpi%7B100%7D%20%5Cleft%20%28%20%

If n is a positive integer, then \left ( \sqrt{3} +1\right )^{2n}-\left ( \sqrt{3}-1 \right )^{2n}is

Option: 1

an irrational number


Option: 2

an odd positive integer


Option: 3

an even positive integer


Option: 4

a rational number other than positive integers


Answers (1)

best_answer

\left ( \sqrt{3}+1 \right )^{2n}-\left ( \sqrt{3}-1 \right )^{2n}

= 2\left [ ^{2n}C_{1}\cdot \left ( \sqrt{3} \right )^{2n-1} +^{2n}C_{3}.\left ( \sqrt{3} \right )^{2n-3}+........\right ]

Now each term has odd power of \sqrt{3}, so all these terms are irrational and thus their sum will also be an irrational number.

Posted by

rishi.raj

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