Figure out this binomial maths question

In the binomial expansion of (2k+x) to the power of n, where k is a constant and n is a positive integer, the coefficient of x squared is equal to th3 coefficient of x cubed.
a) prove that n =6k+2
b) given also that k = 2/3 expand (2k+x) in ascending powers of x up to and including the term x cubed, giving each coefficient as an exact fraction in its simplest form.
Thanks

Reply 1

ZdYnm8vuNR

13

What part are you struggling with? Have you done any progress so far? I don't want to just do your maths hw.

Reply 2

Shiverhawk

OP

8

It's not homework I was practising for my mock in January and I came across this question. I have done this chapter but I don't know what to do if there are 2 unknowns. Any help will be appreciated.(

Reply 3

Shiverhawk

OP

8

Original post by ZdYnm8vuNR

What part are you struggling with? Have you done any progress so far? I don't want to just do your maths hw.

It's not homework I was practising for my mock in January and I came across this question. I have done this chapter but I don't know what to do if there are 2 unknowns. Any help will be appreciated.(

Reply 4

ZdYnm8vuNR

13

Original post by Shiverhawk

It's not homework I was practising for my mock in January and I came across this question. I have done this chapter but I don't know what to do if there are 2 unknowns. Any help will be appreciated.(

Ok so as the question states that the coefficient of x^2 is equal to the coefficient of x^3, we can make the coefficients equal to eachother. To get the expression for the coefficients use the binomial expansion formula (nCr * 2k^(n-r) * x^r )

Reply 5

Shiverhawk

OP

8

Original post by ZdYnm8vuNR

Ok so as the question states that the coefficient of x^2 is equal to the coefficient of x^3, we can make the coefficients equal to eachother. To get the expression for the coefficients use the binomial expansion formula (nCr * 2k^(n-r) * x^r )

I don't know what to do next

Reply 6

ZdYnm8vuNR

13

Original post by Shiverhawk

I don't know what to do next

To be honest, im kind of lost also. I feel like I've overcomplicated something and im stuck. What I did is expand the n choose 3 into factorial form and simplify, but I can't get n in terms of k

Reply 7

Shiverhawk

OP

8

Original post by ZdYnm8vuNR

To be honest, im kind of lost also. I feel like I've overcomplicated something and im stuck. What I did is expand the n choose 3 into factorial form and simplify, but I can't get n in terms of k