The coefficient of x^2 in the expansion (k+1/3x)^5 is 30. Find the value of the constant k.

I have almost absolutely no idea how to do this... Please help!

Question

The coefficient of x^2 in the expansion (k+1/3x)^5 is 30. Find the value of the constant k.

I have almost absolutely no idea how to do this... Please help!

anonymous · Answer

This involves pascall's triangle.

anonymous · Answer

What exactly about it is Pascal, is it something to do with binomial expansion?

anonymous · Answer

$$
Ck^3\left(\frac 13 x\right)^2 = 30x^2
$$

anonymous · Answer

In this case $$
C  = \binom 53=\binom 52
$$

anonymous · Answer

You could use Pascal's triangle to find the binomial coefficient.

anonymous · Answer

Or you could use the combination function if you already know it.

anonymous · Answer

So would it be something like
5C3 x k^2 x (1/3x)^2=30?

anonymous · Answer

=30x^2

anonymous · Answer

Why is it 30x^2?

anonymous · Answer

Trust me, you don't want $x$ in your answer.  It said $30$ is only the coefficient of the $x^2$ term, so the whole term is $30x^2$

anonymous · Answer

Hmm ok, so
5C3 x k^2 x (1/3x)^2=30x^2
Do I just solve that?

anonymous · Answer

Yes.

anonymous · Answer

Ok thank you for your help.

anonymous · Answer

http://www.wolframalpha.com/input/?i=%285+choose+3%29+*+k%5E3+*+%281%2F3%29%5E2%3D30

anonymous · Answer

Thanks so much!!!