Question: If in the expansion of $\left( \sqrt{3} + \sqrt[8]{5} \right)^{256}$, the coefficients of \(a_{r}\...

Question

If in the expansion of $\left( \sqrt{3} + \sqrt[8]{5} \right)^{256}$ , the coefficients of $a_{r}$ and $x^{r}$ be equal, then r is equal to.

Answer 1

$\frac{(2n)!3!3!}{(2n - m)!}$

$\frac{(2n)!}{\left( \frac{2n - m}{3} \right) ⥂ !\left( \frac{4n + m}{3} \right)!}$ Coefficient of $(1 + x)^{n}$ and coefficient of

$n^{2} - 9n$

So, we must have $(1 + x + x^{3} + x^{4})^{10},$ .

Question: If in the expansion of \(\left( \sqrt{3} + \sqrt[8]{5} \right)^{256}\), the coefficients of \(a_{r}\...