SOLUTION: if the 21st and 22nd terms in the expansion of (1+x)^44 are equal, find the value of x

Algebra ->  Exponents -> SOLUTION: if the 21st and 22nd terms in the expansion of (1+x)^44 are equal, find the value of x      Log On


   

Question 730767: if the 21st and 22nd terms in the expansion of (1+x)^44 are equal, find the value of x
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53426) About Me  (Show Source):
You can put this solution on YOUR website!
.
if the 21st and 22nd terms in the expansion of (1+x)^44 are equal, find the value of x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The 21th term is  C(44,20)*x^20 = %2844%21%2F%2820%21%2A24%21%29%29%2Ax%5E20.


The 22th term is  C(44,21)*x^21 = %2844%21%2F%2821%21%2A23%21%29%29%5Ex%5E21.


They are equal

    %2844%21%2F%2820%21%2A24%21%29%29%2Ax%5E20 = %2844%21%2F%2821%21%2A23%21%29%29%5Ex%5E21.


It implies

    %2821%21%2A23%21%29%2F%2820%21%2A24%21%29 = x,

or

    x = 21%2F24 = 7%2F8.



ANSWER.  x = 7%2F8.

Solved.

-------------------------

The answer in the post by @lynnlo is incorrect.
Simply ignore his post.