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#1 2007-05-28 16:56:19

nkdlunch
Guest

What is M?

untitled-1.jpg








This is a real stumper. The square root of 1 minus 1 over m plus the square root of minus 1 over m =m

Solve for M.

M is a variable.

Directions on how the ansewer was reached, if it ever is, wold be great.

#2 2007-05-28 16:58:24

nkdlunch
Guest

Re: What is M?

Sorry for the bad drawing and bad spelling.

#3 2007-05-28 19:27:07

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

Re: What is M?

There is no actual solution to this problem, but I'll show you what I would normally have done algebraically to solve it:







m ≈ -2.3829757691

But as I said, there is no solution. Substitute m into the LHS of the equation and you will not get m.

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#4 2007-05-28 22:05:07

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

Re: What is M?

Identity wrote:

There is no actual solution to this problem …

There is no real solution to the problem – but might m be complex?

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#5 2007-05-28 22:51:48

LQ
Real Member
Registered: 2006-12-04
Posts: 1,285

Re: What is M?

For goodness sake, it's a third degree equation, all 3-power equations have 3 solutions. they might not be real, but they are actual
"might m be complex"

it is called "may", not "might". If they may not there is no right solution, only wrong or "bad" solutions. Even if they are bad they might not be complex, they are complex.

Last edited by LQ (2007-05-29 00:35:59)


I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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#6 2007-05-28 23:35:07

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

Re: What is M?

Look, what is the matter with you?

I was only suggesting that m in the original problem (the one with two square roots) might be allowed to be complex, not just real. Identity claims that the problem has no solution. Well, if m is required to be real, then indeed the problem has no solution. But if m is allowed to take on complex values, then things might be different. (I haven’t gone all the way to compute the complex values, so I’m only speaking tentatively.)

What’s more, you misspelled “goodness”.

Last edited by JaneFairfax (2007-05-28 23:40:36)

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#7 2007-05-28 23:57:19

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

Re: What is M?

LQ wrote:

For godness sake, it's a third degree equation, all 3-power equations have 3 solutions.

But the problem is that the cubic equation that Identity found isn't completely equivalent to the original, because he squared both sides at one point in order to reach that stage, and you can't work backwards from that. Yes, a cubic will always have 3 solutions, but Identity already found one and showed that it didn't work for the original question.

In Identity's working, the furthest step that you can get back to the start from is this one:

And it's not too hard to see that that can't have a real solution.

PS. I would say that 'might' makes more sense than 'may'. tongue


Why did the vector cross the road?
It wanted to be normal.

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#8 2007-05-29 01:00:14

nkdlunch
Guest

Re: What is M?

Identity wrote:

There is no actual solution to this problem, but I'll show you what I would normally have done algebraically to solve it:







m ≈ -2.3829757691

But as I said, there is no solution. Substitute m into the LHS of the equation and you will not get m.

What is LHS?
And what would I'd have to say to show how it was solved?

#9 2007-05-29 02:30:36

LQ
Real Member
Registered: 2006-12-04
Posts: 1,285

Re: What is M?

(a + b)^3 = a^3 + b^3 + 3ab^2 + 3ba^2 = 3ab(a+b) + (a + b)^3 + a^3 + b^3

3ab = -4
a^3 + b^3 = 4 = 3ab
a = -4/3b

(-4/3b)^3 + b^3 = 4

-(4/3)^3 + b^6 = 4b^3
(b^3)^2 - b^3 + -(4/3)^3 = 0

b^3 = 1/2 +/- sqrt(1/4+4/3^3)
figure out a in the same way as b and a + b = m

If no solutions work, there is only false solutions.

Last edited by LQ (2007-05-29 04:50:24)


I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

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#10 2007-05-29 02:43:29

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

Re: What is M?

nkdlunch wrote:
Identity wrote:

There is no actual solution to this problem, but I'll show you what I would normally have done algebraically to solve it:







m ≈ -2.3829757691

But as I said, there is no solution. Substitute m into the LHS of the equation and you will not get m.

What is LHS?
And what would I'd have to say to show how it was solved?

It depends whether or not you've learnt about complex numbers.

Last edited by Identity (2007-05-29 02:45:22)

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#11 2007-05-29 04:30:57

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

Re: What is M?

LHS is left hand side.  RHS, other than being right hand side, are my initials.  When I first saw a professor write that on the board and wasn't quite paying attention, I freaked out a little.


"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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#12 2007-05-29 09:31:43

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: What is M?

How funny ... that would have been freaky!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#13 2007-05-30 15:50:51

nkdlunch
Guest

Re: What is M?

Thanks. Maybe these suggestions will help.

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