The sum of all rational terms in the expansion of (2 +$\sqrt{3}$) is 8
Step-by-Step Solution
Key Concept: Use the general term of the binomial expansion for rational terms$i_n$binomial expansion and impose the required coefficient or exponent condition.
$S = (2$+$\sqrt{3}$) 8 (4) For sum of rational terms 8 8 8 6 2 8 4 4 =$C_{0}$(2) +$C_{2}$(2)$\cdot$($\sqrt{3}$) +$C_{4}$(2) ($\sqrt{3}$) 8 2 6 8 8 +$C_{6}$(2) ($\sqrt{3}$) +$C_{8}$($\sqrt{3}$) 8 6 4$2 = 2 + 28$$\times$ 2$\cdot$$3 + 70.2$$\cdot$$9 + 28.2$$.27 + 81 = 256 + 5376 + 10080 + 3024 + 81 = 18817$
Correct Answer: 4