Thread: 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 ???

Hey mido22.

Can you show your working for the problems?

1) --> from binomial theorem


since


so


so x= zero or 0.5 or 4.5 since or

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

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.

Hello, mido22!

2) If the ratio between the two middle terms in the expansion of is
find the value of

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.

Thanks (Soroban and chiro) very much