The sixth term in the expansion of left(3-sqr | vedclass

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(D) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$. For the expansion of $\left(3-\sqrt{\frac{17

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negative irrational number

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(D) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $T_{r+1} = {}^nC_r a^{n-r} b^r$. For the expansion of $\left(3-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^{10}$,we have $n=10$,$a=3$,and $b=-\sqrt{\frac{17}{4}+3 \sqrt{2}}$. The sixth term $(T_6)$ corresponds to $r=5$: $T_6 = {}^{10}C_5 (3)^{10-5} \left(-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^5$. $T_6 = -{}^{10}C_5 (3)^5 \left(\frac{17}{4}+3 \sqrt{2}\right)^{5/2}$. Since $\sqrt{2}$ is irrational,any power of $\left(\frac{17}{4}+3 \sqrt{2}\right)$ involving a fractional exponent will remain irrational. Thus,$T_6$ is a negative irrational number.

The sixth term in the expansion of $\left(3-\sqrt{\frac{17}{4}+3 \sqrt{2}}\right)^{10}$ is a

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