Is this cool with you?

bobbym · 2011-06-11 02:27:41

You mean ignorant and ignorant of it.

I have seen people who are ignorant and adamant.

How could you? They all live here.

gAr · 2011-06-11 03:24:31

Yes!

How could you? They all live here.

May not be all of them, they are randomly and non-uniformly distributed, each possessing ignorance in different quantities!

I was trying http://www.mathisfunforum.com/viewtopic.php?id=15630,
how to solve x^(1/x) == 243, numerically?
I did not understand the output of wolframalpha, and newton raphson method doesn't seem to give the right answer.

bobbym · 2011-06-11 10:54:31

Hi gAr;

You probably solved it symbolically. Few equations really can be solved like that. This one involves the Product Log.

Wolfram has an NSolve and FindRoot command. I believe Sage does to ( Find_root). These work numerically. Here is another way that works in this case:

Enter "x^(1/x)==243"

You will see a solution and a button marked Approximate Form.

Click that and you will get.

.166623 - .364093i you can now get more digits by clicking the More Digits button. You should be able to use Newtons Iteration on that as an initial guess.

gAr · 2011-06-11 16:58:35

Hi bobbym,

I think find_root in sage works only for reals.

Anyway, I found a way to output the approximate solutions in wolfram, I took one of the productlog solutions and entered the command :
Table[N(e^(-ProductLog[-5 log(3) - 2 i n pi])),{n,10}]

But still, it's difficult to solve for A, B, C subject to condition A*B*C = 1.
Now I'm beginning to doubt whether it has a solution at all !

bobbym · 2011-06-11 17:28:35

Hi gAr;

Are those solutions?

gAr · 2011-06-11 17:40:33

Those are solutions for the equation x^(1/x) = 243

I'm trying to find x,y,z such that x^(1/x) = y^(1/y) = z^(1/z) = 243 and x*y*z = 1
Do you think it's possible to have a solution?

bobbym · 2011-06-11 18:14:58

Hi gAr;

That is the question that has been posed on this forum. I have stayed out of it because I do not think the OP knows the right answer, or even knows if there is one.

gAr · 2011-06-11 18:24:31

Hi bobbym,

Yes, and I don't know whether the OP was serious, after looking at some of his replies!
Anyway, I'm just curious.

bobbym · 2011-06-11 18:34:24

Hi gAr;

It looks like there are an infinite number of solutions, all of which are imaginary numbers.

gAr · 2011-06-11 18:40:12

I was trying to find atleast one such (x,y,z) pair, still not able to find one.

bobbym · 2011-06-11 19:04:36

I have not found one either. Each time I manipulate your equations and get a solution it never works when plugged in.

gAr · 2011-06-11 19:47:29

Same with me.

Manipulating it, I got another condition:

Then I thought it's sufficient to solve xyz=1 and x+y+z=0.
But strangely, the solutions didn't work!

bobbym · 2011-06-12 00:38:28

Hi gAr;

No solutions that I can find.

gAr · 2011-06-12 00:48:32

Hi bobbym,

Ok, no problem.

bobbym · 2011-06-12 01:15:04

Hi gAr;

Everything I am doing looks fruitless. It could be that there are not any solutions.

gAr · 2011-06-12 01:34:25

Hi bobbym,

Yes, that's what I think too.
I think I'll go crazy if I try it any longer!

bobbym · 2011-06-12 01:59:06

I know what you mean!

bobbym · 2011-06-23 00:38:51

New Problem!

A believes he can stump our panel, even though he is on it! But he dislikes B and E so much he can not help himself. He poses this:

Each person is to get an equal amount of gold and an equal number of sacks. The sacks are of three types. Empty, half full and full. There are n of each type. So if n = 2 then there are (empty) (empty) ( half full ) ( half full ) ( full ) ( full ).

One way to split the gold with those 6 sacks is

Person 1) ( full ) ( empty )
Person 2) ( full ) ( empty )
Person 3) ( half full ) ( half full )

They each have the same amount of gold and the same number of sacks. How many ways are there if n = 100. Can you find a general formula for any n?

A says) I have stumped you all! Including myself!
B says) You are losing it A! Calm down and let me work on it.
C says) I got it. 182763548917624567373891872653412 ways
D says) That is incorrect.
E says) That is not even close and where is your general formula?

gAr · 2011-06-23 00:50:16

Hi bobbym,

Can they all get only empty sacks?(No gold to any of them)

bobbym · 2011-06-23 00:54:33

Hi;

No, you want to split the gold equally among the three of them.

gAr · 2011-06-23 01:03:46

Okay, I think I misunderstood the question.

For n=2, there are 3 units of gold.
For n=3, (empty) (empty)(empty) ( half full ) ( half full ) ( half full ) ( full ) ( full ) ( full ) : 4.5 units of gold, and we need to share it equally... like that?

bobbym · 2011-06-23 01:05:59

Hi gAr;

Yes. Each one would now need to get 1.5 units of gold and 3 sacks.

gAr · 2011-06-23 01:13:23

Hi bobbym,

Okay, thanks.

Let me check:
n=1, 0 ways.
n=2, 3 ways.
n=3, 1 way
?

bobbym · 2011-06-23 01:20:39

Hi gAr;

I do not have a working program for this yet. The one I was using had a bug in it so I have to rewrite it. I do not have a table of answers yet.

gAr · 2011-06-23 01:25:23

Okay.
But these small cases can be done by hand.
I'm asking to verify whether I understood it correctly.

Math Is Fun Forum

#651 2011-06-11 02:27:41

Re: Is this cool with you?

#652 2011-06-11 03:24:31

Re: Is this cool with you?

#653 2011-06-11 10:54:31

Re: Is this cool with you?

#654 2011-06-11 16:58:35

Re: Is this cool with you?

#655 2011-06-11 17:28:35

Re: Is this cool with you?

#656 2011-06-11 17:40:33

Re: Is this cool with you?

#657 2011-06-11 18:14:58

Re: Is this cool with you?

#658 2011-06-11 18:24:31

Re: Is this cool with you?

#659 2011-06-11 18:34:24

Re: Is this cool with you?

#660 2011-06-11 18:40:12

Re: Is this cool with you?

#661 2011-06-11 19:04:36

Re: Is this cool with you?

#662 2011-06-11 19:47:29

Re: Is this cool with you?

#663 2011-06-12 00:38:28

Re: Is this cool with you?

#664 2011-06-12 00:48:32

Re: Is this cool with you?

#665 2011-06-12 01:15:04

Re: Is this cool with you?

#666 2011-06-12 01:34:25

Re: Is this cool with you?

#667 2011-06-12 01:59:06

Re: Is this cool with you?

#668 2011-06-23 00:38:51

Re: Is this cool with you?

#669 2011-06-23 00:50:16

Re: Is this cool with you?

#670 2011-06-23 00:54:33

Re: Is this cool with you?

#671 2011-06-23 01:03:46

Re: Is this cool with you?

#672 2011-06-23 01:05:59

Re: Is this cool with you?

#673 2011-06-23 01:13:23

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#674 2011-06-23 01:20:39

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#675 2011-06-23 01:25:23

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