(3+sqrt{8})^5+(3-sqrt{8})^5= | vedclass

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(C) Using the binomial expansion $(a+b)^n + (a-b)^n = 2 \sum_{k=0, 2, 4, \dots} \binom{n}{k} a^{n-k} b^k$. Here,$a=3$,$b=\sqrt{8}$,and $n=5$. $(3+\sqr

Vedclass · Accepted Answer

$6726$

Vedclass · Answer

(C) Using the binomial expansion $(a+b)^n + (a-b)^n = 2 \sum_{k=0, 2, 4, \dots} \binom{n}{k} a^{n-k} b^k$. Here,$a=3$,$b=\sqrt{8}$,and $n=5$. $(3+\sqrt{8})^5+(3-\sqrt{8})^5 = 2 \left[ \binom{5}{0} 3^5 + \binom{5}{2} 3^3 (\sqrt{8})^2 + \binom{5}{4} 3^1 (\sqrt{8})^4 ight]$. $= 2 \left[ 1 \cdot 243 + 10 \cdot 27 \cdot 8 + 5 \cdot 3 \cdot 64 ight]$. $= 2 \left[ 243 + 2160 + 960 ight]$. $= 2 	imes 3363 = 6726$.

$(3+\sqrt{8})^5+(3-\sqrt{8})^5=$

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