The coefficient of $$\(\frac{1}{x}\)$$ in the expansion of $$\(\left(k x+\frac{1}{x}\right)^{5}+\left(1-\frac{2}{x}\right)^{8}\)$$ is 74 . Find the value of the positive constant $$\(k\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_s20_qp_11 Year：2020 Question No：2
Answer:
\[
\left(k x+\frac{1}{x}\right)^{5}+\left(1-\frac{2}{x}\right)^{8}
\]
Coefficient in \(\left(k x+\frac{1}{x}\right)^{5}=10 \times k^{2}\)
(B1 for 10. B1 for \(k^{2}\) )
Coefficient in \(\left(1-\frac{2}{x}\right)^{8}=8 \times-2\)
\[
10 k^{2}-16=74 \rightarrow k=3
\]
\left(k x+\frac{1}{x}\right)^{5}+\left(1-\frac{2}{x}\right)^{8}
\]
Coefficient in \(\left(k x+\frac{1}{x}\right)^{5}=10 \times k^{2}\)
(B1 for 10. B1 for \(k^{2}\) )
Coefficient in \(\left(1-\frac{2}{x}\right)^{8}=8 \times-2\)
\[
10 k^{2}-16=74 \rightarrow k=3
\]
Knowledge points:
1.6.1 use the expansion of , where is a positive integer (Including the notations and n!) (Knowledge of the greatest term and properties of the coefficients are not required.)
Solution:
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