Math Is Fun Forum
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#26 2015-05-05 05:05:02
Re: 21 Questions from Amrita
Is that solution aesthetically pleasing to you?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#27 2015-05-05 05:11:04
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
In some ways yes, here is why.
1) It is the first solution, meaning it took the least amount of time. Time is money.
2) It is unlikely that it is marred by an arithmetic mistake.
3) It is experimental in nature.
4) The mathematicians obsession with beauty I believe places an unnecessary burden.
Multiplying that out by hand is Kaboobly Doo.
Not true, Frank's proof is the only possible way so why not multiply?
Anyways, there will be other proofs to this question provided soon.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#28 2015-05-05 05:22:20
Re: 21 Questions from Amrita
Set both factors equal to 0 and leave out the 1 / 4.
Why must both factors be 0?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#29 2015-05-05 05:23:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
That is to proceed with the elimination of the z variable. Whether we do it by hand or by M, I need it in that form.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#30 2015-05-05 05:30:08
Re: 21 Questions from Amrita
I don't understand. What if one of them is not 0?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#31 2015-05-05 05:31:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
Remember f(x,y,z) = 0, that is given. When you factor a quadratic you set both factors equal to 0 to solve.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#32 2015-05-05 05:34:23
Re: 21 Questions from Amrita
For example?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#33 2015-05-05 05:47:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
f(x) = x^2 + 3x + 2 = 0
f(x) = (x + 1)(x + 2) = 0
( x + 1 ) = 0
( x + 2) = 0
Solving both, x = -1 and x = - 2
To prove that I found the roots in your question, just plug in to f(x,y,z). You will get 0.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#34 2015-05-05 06:02:33
Re: 21 Questions from Amrita
( x + 1 ) = 0
( x + 2) = 0
Note that only one of them is true
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#35 2015-05-05 06:03:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
Both of them are true.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#36 2015-05-05 06:13:27
Re: 21 Questions from Amrita
If both of them were true x = -1 = -2
Or, following your idea
Subtract the equations from each other, you should get -1 = 0
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#37 2015-05-05 06:15:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
If both of them were true x = -1 = -2
The roots of the equation have been found. The roots are defined as the values that make the equation true.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#38 2015-05-05 06:17:46
Re: 21 Questions from Amrita
Of course they both are roots but that does not mean both those equations are true
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#39 2015-05-05 06:20:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
I did not say they were both true but when you put x = - 2 or x = - 1 they then are true.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#40 2015-05-05 06:21:40
Re: 21 Questions from Amrita
That is not the point.
Can you subtract the equations?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#41 2015-05-05 06:22:57
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
They are not meant to be subtracted, they are factors and one or both of them must be 0.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#42 2015-05-05 06:25:57
Re: 21 Questions from Amrita
How do you eliminate z?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#43 2015-05-05 06:29:30
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
Everytime I have been asked to do that manually I always did it but it took a long time. I used M to do it. But you are missing the point, it was proved by plugging in that x, 3x and 5x are roots of that equation you gave.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#44 2015-05-05 06:33:57
Re: 21 Questions from Amrita
You need to convince me that they are the only roots
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#45 2015-05-05 06:37:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
As far as I know when you factor and solve there may be extraneous or false roots. That is why you plug in to check but there are never roots that are not in those factors. In this case we get a family of roots, they are built from the parameter x.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#46 2015-05-05 06:47:59
Re: 21 Questions from Amrita
Let us look at a new question
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#47 2015-05-05 06:50:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
You have not asked the most important question, the one that has a simple proof.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#48 2015-05-05 07:01:14
Re: 21 Questions from Amrita
Can you ask that question on behalf of me?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#49 2015-05-05 07:02:11
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: 21 Questions from Amrita
The one about the differences...
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#50 2015-05-06 00:17:03
Re: 21 Questions from Amrita
Hm?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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