SOLUTION: Solve for n: {{{matrix(1,3, 4*(matrix(2,1,n,2)), ""="", (matrix(2,1,n+2,3)))}}}

Algebra ->  Probability-and-statistics -> SOLUTION: Solve for n: {{{matrix(1,3, 4*(matrix(2,1,n,2)), ""="", (matrix(2,1,n+2,3)))}}}      Log On


   



Question 1170989: Solve for n:

Found 3 solutions by ikleyn, Alan3354, Edwin McCravy:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Without a full,  complete and accurate wording description,  this post  MAKES  no  SENSE.


So,  I deleted it.


===========

Edwin,  in your post,  I see some invectives to my address.

May be,  it is a form of humor,  which I do not understand //(or,  may be,  it is not a form of humor . . . ).


But first,  I see that the input/(the post)  was edited by you and has nothing in common with
the original post,    which   I   REALLY   deleted;    and

the second,  I just gave a word to myself do not comment your posts.


Stay safe . . .




Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Do you have a question?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Hey, tutors, you two should be ashamed of yourselves! Leave this student alone!
Those parentheses he or she had up there meant combinations, or if you prefer,
binomial coefficients.  I rewrote it up there like he/she obviously meant it. 

%28matrix%282%2C1%2CN%2CK%29%29 means the same as C(N,K) or NCK. 

The simplest way to evaluate combinations, or binomial coefficients, is not by
using the definition, which is: 

%28matrix%282%2C1%2CN%2CK%29%29=+N%21%2F%28K%21%28N-K%29%21%29 

but by this:

, where there are the same number of factors in the numerator 
as in the factorial (K!) in the denominator.

So









Divide both sides by n:



matrix%281%2C3%2C%0D%0A%0D%0A12n-12%2C%0D%0A%22%22=%22%22%2C%0D%0An%5E2%2B3n%2B2%29%29


matrix%281%2C3%2C%0D%0A%0D%0A0%2C%0D%0A%22%22=%22%22%2C%0D%0An%5E2-9n%2B14%29%29

matrix%281%2C3%2C%0D%0A%0D%0A0%2C%0D%0A%22%22=%22%22%2C%0D%0A%28n-7%29%28n-2%29%29

n-7=0; n-2=0
  n=7;   n=2

So there are two solutions.

They both check:






matrix%281%2C3%2C%0D%0A%0D%0A4%2A21%2C%0D%0A%22%22=%22%22%2C%0D%0A84%29%29

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





matrix%281%2C3%2C%0D%0A%0D%0A4%2A1%2C%0D%0A%22%22=%22%22%2C%0D%0A4%29%29

Edwin