+0  
 
0
104
5
avatar

What is the constant term of the expansion of \(\left(6x+\dfrac{1}{3x}\right)^6\)?

 May 18, 2020
 #1
avatar+927 
0

What's the constant term of the expansion of (do + not + cheat + on + your) * (A*o*P*S + Homework) ?

 May 18, 2020
 #2
avatar+110699 
-1

Let up Hugo,

this is a standard maths question that could have come from any school or text book anywhere in the world.

Melody  May 19, 2020
 #3
avatar+927 
-1

Hi Melody, while this may appear to be one, I perfectly recall this from being in... the lesson about "simon's favorite factoring trick" or +/- one lesson.

 

However I do understand that there are similar questions not property of AoPS and if I hadn't taken that particular course I would have thought it wasn't one, but I do remember having trouble with this one.

hugomimihu  May 19, 2020
 #4
avatar+110699 
-1

So what? 

 

Students all over the whole world have been having trouble with this one for over a hundred years. 

It is a completely standard question.

 

I do not even know why this is an AoPS question at all.  It is not problem-solving, it is a standard algebraic question.

Melody  May 19, 2020
edited by Melody  May 19, 2020
 #5
avatar+110699 
0

 

\(\left(6x+\dfrac{1}{3x}\right)^6\\~\\ T_n=\begin{pmatrix} 6\\ n \end{pmatrix} (\frac{1}{3x})^n(6x)^{n-6}\\ \text{If you pull out the x terms you get } (\frac{1}{x})^n*x^{n-6} \\ \text{The constant term will have }x^0\qquad\\ \text{So solve for n}\\ etc\)

 

 

Please no other answerer finish this. 

.
 May 19, 2020
edited by Melody  May 19, 2020

58 Online Users

avatar
avatar
avatar