SOLUTION: Don't know how to this equation.. can someone help me? Solve the following equation for n nC2 - 5{P(1/3n, 2)} + 1/3n = 9

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Question 1042916: Don't know how to this equation.. can someone help me?
Solve the following equation for n
nC2 - 5{P(1/3n, 2)} + 1/3n = 9

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
Don't know how to this equation.. can someone help me?
Solve the following equation for n
nC2 - 5{P(1/3n, 2)} + 1/3n = 9
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

n = 9.


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Comment from student: Thanks a lot ikleyn!! Can you give me the steps on how you found nine please. So that I can understand better.
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It is clear that %281%2F3%29%2An must be integer positive.

Therefore, let us introduce new variable m = %281%2F3%29n.

Then n = 3m,  and the equation takes the form

(3m)C2 - 5P(m,2) + m = 9.

Or  %283m%2A%283m-1%29%29%2F2 - 5*m*(m-1) + m = 9.

This is a quadratic equation, and you can solve it.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Don't know how to this equation.. can someone help me?
Solve the following equation for n
nC2 - 5{P(1/3n, 2)} + 1/3n = 9
The following quadratic ensues: n%5E2+-+27n+%2B+162+=+0, which means that: highlight_green%28matrix%281%2C3%2C+n+=+9%2C+or%2C+n+=+18%29%29