The coefficient of $$\(\frac{1}{x}\)$$ in the expansion of $$\(\left(2 x+\frac{a}{x^{2}}\right)^{5}\)$$ is 720 . Find the possible values of the constant $$\(a\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：6(a)
Answer:
\(5 \mathrm{C} 2[2(x)]^{3}\left[\frac{a}{\left(x^{2}\right)}\right]^{2}\)
\(10 \times 8 \times a^{2}\left(\frac{x^{3}}{x^{4}}\right)=720\left(\frac{1}{x}\right)\)
\(a=\pm 3\)
\(10 \times 8 \times a^{2}\left(\frac{x^{3}}{x^{4}}\right)=720\left(\frac{1}{x}\right)\)
\(a=\pm 3\)
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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