SOLUTION: If 3n³× (n-2)! + 6n - 3n² × (n-3)!

SOLUTION: If 3n³× (n-2)! + 6n - 3n² × (n-3)! - 360 = 0 , find value of n ?

Question 1206590: If 3n³× (n-2)! + 6n - 3n² × (n-3)! - 360 = 0 , find value of n ?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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If 3n³× (n-2)! + 6n - 3n² × (n-3)! - 360 = 0 , find value of n ?
~~~~~~~~~~~~~~~~

   +  -  - 360 =

= .. + 6n - 360.


Now you can see that this expression is monotonically growing function of n.

So, if we guess one solution, it will provide a UNIQUE solution.


It is not difficult to guess one solution. It is n= 4, because

    .. + 6*4 - 360 = 3*16*7*1 + 24 - 360 = 0.


So, the ANSWER to the problem is n= 4.

Solved.

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In such problems, guessing of a root in combinations with monotonicity
of a function turns guessing in strict mathematical proof.

In other words, in this combination, guessing of a root acquires
the force and the status of a valid mathematical proof.

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