Question

Question #7b7eb

Answer 1

`20412`.

Explanation:

The question is : How to find the constant term in the expansion of
`(3/x-x^3)^8`,

The correct `t_(r+1)=""_8C_r(3/x)^(8-r)*(-x^3)^r`,

& NOT `""_8C_r(3/x)^(8-r)*(x^3)^r, "as stated in the Problem"`

`:. t_(r+1)=""_8C_r(3)^(8-r)(x^-1)^(8-r)(-1)^r(x^(3r))`

`=""_8C_r(-1)^r(3)^(8-r)(x^(r-8+3r))`

`=""_8C_r(-1)^r(3)^(8-r)(x^(4r-8))`

For the constant term, the index of `x`, which is `(4r-8)` in our

case, must be `0`.

`:. 4r-8=0 rArr r=2`

`:. "The reqd. constant term"=t_3=""_8C_2(-1)^2(3)^6(x^0)`

`=28*729=20412`.

Enjoy Maths.!