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**solve in R**

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**tony123****Member**- Registered: 2007-08-03
- Posts: 197

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

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,844

tony123,

Squaring both sides,

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

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

Be careful!

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,844

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

sorry ganesh

i think there is still mistake.

http://gyan.talkacademy.com.np

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,844

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

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

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:

Wrap it in bacon

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,844

TheDude,

I shall check again in leisure!

Thanks, all of you, for correcting me!

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

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

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

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

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

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)*

Wrap it in bacon

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

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

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

Good point mathsyperson, I should have been more clear.

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

Wrap it in bacon

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