Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

solve in R

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

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)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

Re: solve in R

tony123,

Squaring both sides,

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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.

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!

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

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!

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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.

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: solve in R

sorry ganesh
i think there is still mistake.

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

Re: solve in R

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

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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.

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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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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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,390

Re: solve in R

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

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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.

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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Identity

Member

Registered: 2007-04-18

Posts: 934

Re: solve in R

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...

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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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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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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saudi_boy

Member

Registered: 2006-11-01

Posts: 41

Re: solve in R

hii all..

my solution

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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