two problems in binomial theorem

1)In the expansion of if where Tn is the term number n

find the values of X that satisfy the given

....My solution : x= 0.5 , 4.5 , 0

Guide answer : 0.5 , 4.5 only ???

2)If the ratio between the two middle terms in the expansion of is 1:4 find the value of X

My solution : x=4 or 0.25

Guide answer : 4 only ???

Re: two problems in binomial theorem

Hey mido22.

Can you show your working for the problems?

Re: two problems in binomial theorem

1) --> from binomial theorem

since

so

so x= zero or 0.5 or 4.5 since or

Re: two problems in binomial theorem

2) because he didn't say in the problem the between t14 to t15 or vice versa

Re: two problems in binomial theorem

For 1) I don't know why they didn't have 0 as a solution: you're answer looks spot on.

For 2) I think they mean successive terms so by this, they mean that the next term is 4 times greater than the previous one.

So basically divide T14/T13 = 4/1 = 4 which gives x = 4.

This is just my interpretation though.

You should ask your teacher for clarification, especially for number 1 in which you gave a good answer. Even your answer for question 2 is a solid one as well.

Re: two problems in binomial theorem

Hello, mido22!

The two middle terms are the 14th and 15th: .

The ratio is: .

I assumed that the ratio was *in that order*: 14th to the 15th.

But I agree that the wording could have been more specific.

I would have allowed full credit (maybe more) for your answer.

It certainly demonstrates innovative thinking.

Re: two problems in binomial theorem

Thanks (Soroban and chiro) very much