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#1 2007-11-11 07:03:23

tony123
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Registered: 2007-08-03
Posts: 192

solve in R

Last edited by tony123 (2007-11-11 07:05:52)

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#2 2007-11-11 23:51:12

Identity
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Registered: 2007-04-18
Posts: 934

Re: solve in R

Edit: This is wrong! But what an elegant problem it would be if my solution was correct!

From this, we can see that only

will work.

Last edited by Identity (2007-11-13 02:14:57)

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#3 2007-11-12 00:15:41

ganesh
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Registered: 2005-06-28
Posts: 25,369

Re: solve in R

tony123,

Squaring both sides,




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#4 2007-11-12 00:21:51

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: solve in R

Ganesh. If you square both sides, the left-hand side is

Be careful! shame

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#5 2007-11-12 00:38:41

ganesh
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Registered: 2005-06-28
Posts: 25,369

Re: solve in R

JaneFairfax,
This is what I get!
Okay, Lets use the substitution method!

Let

The original equation becomes

squaring both sides,

Feed this back in the original equation,

PS:- Struggling with LaTeX! Its been a long break! I refer the tags! When I don't I make mistakes! I shall learn very soon!


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#6 2007-11-12 00:56:38

gyanshrestha
Member
Registered: 2007-11-06
Posts: 41

Re: solve in R

sorry ganesh
i think there is still mistake.


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#7 2007-11-12 00:59:16

ganesh
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Registered: 2005-06-28
Posts: 25,369

Re: solve in R

gyanashreshta,
Mistake in Exponents?
Operation of Exponents?
Or is it only the LaTeX?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#8 2007-11-12 01:00:33

gyanshrestha
Member
Registered: 2007-11-06
Posts: 41

Re: solve in R

what if  we let    y    =   (x)^(x^1/2)-1/2=o and solve it graphically?



i think
(that the answer will be the intersection of x axis and the  curve line given by the new  equation.)

Last edited by gyanshrestha (2007-11-12 01:02:17)


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#9 2007-11-12 03:29:47

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: solve in R

ganesh, you're still making the same mistake.  You're right that

but remember that


Identity, you also made a slight error.

Instead, we need to do this:


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#10 2007-11-12 19:27:17

ganesh
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Registered: 2005-06-28
Posts: 25,369

Re: solve in R

TheDude,
I shall check again in leisure!
Thanks, all of you, for correcting me!


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#11 2007-11-12 23:41:47

gyanshrestha
Member
Registered: 2007-11-06
Posts: 41

Re: solve in R

i don't know the general solution of this equation. the trivial solution is x = 1/4.


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#12 2007-11-13 02:28:53

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: solve in R

gyanshrestha wrote:

i don't know the general solution of this equation. the trivial solution is x = 1/4.

very nice inspection, similarly you can find the solution

Using logs, I arrived at

It looks as if the graph of the RHS is a convex graph, so the graphs only intersect twice.

But it would be awesome if someone posted an analytic solution...

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#13 2007-11-14 15:57:37

gyanshrestha
Member
Registered: 2007-11-06
Posts: 41

Re: solve in R

can we say that if x^x = a^a, then x=a?i if then
above equation can be simplified to

x^x=1/16
and x^x = (1/4)^(1/4)
then we can say that x = 1/4


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#14 2007-11-15 00:47:10

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: solve in R

Sorry gyanshrestha, but x^x = a^a does not imply x = a.   Consider: 0^0 = 1 = 1^1.

Also, (1/4)^(1/4) != 1/16.  (1/4)^2 = 1/16.

Last edited by TheDude (2007-11-15 00:48:22)


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#15 2007-11-15 10:38:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: solve in R

0^0 is indeterminate, so you can't say it's equal to 1.
Also, x^x = a^a does imply that x=a is a solution, it just doesn't guarantee that there aren't others.


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It wanted to be normal.

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#16 2007-11-15 13:04:40

saudi_boy
Member
Registered: 2006-11-01
Posts: 41

Re: solve in R

hii all..

my solution

0c1794705b.jpg

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#17 2007-11-16 00:50:19

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: solve in R

Good point mathsyperson, I should have been more clear.

saudi_boy, you're making the same mistake ganesh made above.


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