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

tony123
Member
Registered: 2007-08-03
Posts: 228

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
Member
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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,954

Re: solve in R

tony123,

Squaring both sides,




It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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

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

JaneFairfax
Member
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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,954

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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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.


http://gyan.talkacademy.com.np

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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,954

Re: solve in R

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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)


http://gyan.talkacademy.com.np

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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

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,954

Re: solve in R

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


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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.


http://gyan.talkacademy.com.np

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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


http://gyan.talkacademy.com.np

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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.


Why did the vector cross the road?
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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