In the expansion of $$\(\left(2 x^{2}+\frac{a}{x}\right)^{6}\)$$, the coefficients of $$\(x^{6}\)$$ and $$\(x^{3}\)$$ are equal. Find the value of the non-zero constant $$\(a\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_11 Year：2020 Question No：5(a)
Answer:
\(6 C 2 \times\left[2\left(x^{2}\right)\right]^{4} \times\left[\frac{a}{(x)}\right]^{2}, 6 C 3 \times\left[2\left(x^{2}\right)\right]^{3} \times\left[\frac{a}{(x)}\right]^{3}\)
\(15 \times 2^{4} \times a^{2}=20 \times 2^{3} \times a^{3}\)
\(a=\frac{15 \times 2^{4}}{20 \times 2^{3}}=\frac{3}{2}\)
\(15 \times 2^{4} \times a^{2}=20 \times 2^{3} \times a^{3}\)
\(a=\frac{15 \times 2^{4}}{20 \times 2^{3}}=\frac{3}{2}\)
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:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download