BINOMIAL THEOREM

9) if (1+ax)^n = 1-10x +40x^2 + terms involving higher poewrs of x,find the values of a and n.
(1+ax)^n
=1+nax+an(n-1)/2(x^2)+ terms involving higher poewrs of x,find the values of a and n.
So
na=-10...(1)
a^2n(n-1)/2=40...(2)
from (2)
-5a(n-1)=40
a(n-1)=-8
an-a=-8
-10-a=-8
a=-2
n=5
13) in the expansion of (x^2 + k/x)^8 ,where k不等如0 .the coefficient of x^7 is equal to the coefficient of 1/x^5 .find the values of k.
The general term is
8Cr(x^2)^(8-r)(k/x)^r
=k^r(8Cr)x^(16-3r)
when 16-3r=7
r=3
the coefficient of x^7
=k^r(8Cr)
=56k^3
when 16-3r=-5
r=7
the coefficient of x^7
=8k^7
since the coefficient of x^7 is equal to the coefficient of 1/x^5
56k^3=8k^7
k^4=7
k=7^(1/4)