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10th Term of the expansion of  \left[3-\sqrt{\frac{21}{4}+3 \sqrt{3}}\right]^{20} is 

Option: 1

A rational number


Option: 2

An irrational number


Option: 3

Negative Integer


Option: 4

Positive Integer


Answers (1)

best_answer

The given term can be written as,

\begin{array}{l}{\left[3-\sqrt{\frac{21}{4}+3 \sqrt{3}}\right]^{20}=\left[3-\sqrt{\left(\frac{3}{2}\right)^{2}+(\sqrt{3})^{2}+2 \times \frac{3}{2} \times \sqrt{3}}\right]^{20}} \\ {=\left[3-\sqrt{\left(\frac{3}{2}+\sqrt{3}\right)^{2}}\right]^{20}} \\ {=\left[\frac{3}{2}-\sqrt{3}\right]^{20}}\end{array}

T_{10}=T_{9+1}=^{20} C_{9}\left(\frac{3}{2}\right)^{20-9} \cdot(-\sqrt{3})^{9}

Here, (-\sqrt{3})^{9} is an irrational number

option B is correct.

Posted by

SANGALDEEP SINGH

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