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#1 2006-05-14 13:20:43

mikau
Member
Registered: 2005-08-22
Posts: 1,504

identity for sqrt (a + b)

Does anyone know if there is ANY identity for sqrt ( a + b) ? It would be super usefull for integration and many other things.


A logarithm is just a misspelled algorithm.

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#2 2006-05-14 18:48:44

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: identity for sqrt (a + b)

Or try to prove that no identity exists.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-05-14 19:30:46

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: identity for sqrt (a + b)

I think not.


IPBLE:  Increasing Performance By Lowering Expectations.

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#4 2006-05-16 04:07:04

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: identity for sqrt (a + b)

The only thing I've come up with is if a and b are both positive, sqrt (a + b) is the hypotenuse of a right triangle whose legs are sqrt(a), sqrt (b).  The only way I know to solve this without using the pythegorean theorem is to find θ.

θ = arctan (sqrt b / sqrt a),   

c = sqrt b/ sin θ  OR  sqrt a / cos θ  = sqrt ( a + b)

but really all we get is sqrt (a + b) = sqrt b / sin [  arctan (sqrt b / sqrt a)  ]

But as a substitution identity thats pretty worthless as it only makes it more complicated.

View Image: sqrtidentity.JPG

Last edited by mikau (2006-05-16 04:07:50)


A logarithm is just a misspelled algorithm.

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#5 2006-05-16 09:27:48

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,552

Re: identity for sqrt (a + b)

I put a square in the center of a square and tried solving for stuff, but after quadratic formula, it came back to sqrt(a + b) again!

Last edited by John E. Franklin (2006-05-16 09:28:32)


igloo myrtilles fourmis

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#6 2006-05-16 09:47:35

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: identity for sqrt (a + b)

Yeah I wasted a lot of time going in circles with this one.


A logarithm is just a misspelled algorithm.

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#7 2006-05-19 00:58:03

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: identity for sqrt (a + b)

This may be helpful (it requires only

and
:
.

Last edited by krassi_holmz (2006-05-19 01:02:31)


IPBLE:  Increasing Performance By Lowering Expectations.

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#8 2006-05-19 04:40:44

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: identity for sqrt (a + b)

Yeah but they are still a sum inside a radical. Ideally an identity similar to something like sin ( a + b) would be nice. For instance: sqrt ( a + b) = sqrt a sqrt b - 1/sqrt b sqrt a  or something like that, that seperates them into individual squareroots.


A logarithm is just a misspelled algorithm.

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#9 2006-05-19 04:54:52

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: identity for sqrt (a + b)

Yeah, I know.
But I don't think we'll go further than


IPBLE:  Increasing Performance By Lowering Expectations.

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