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#1 2009-04-23 10:18:50
- tony123
- Member
- Registered: 2007-08-03
- Posts: 229
Determine all solutions
Determine all solutions in real numbers a,b,c,d of the system
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#2 2009-04-24 03:44:57
- TheDude
- Member
- Registered: 2007-10-23
- Posts: 361
Re: Determine all solutions
Last edited by TheDude (2009-04-24 03:49:16)
Wrap it in bacon
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#3 2009-04-24 04:54:41
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Determine all solutions
Nice work! One small flaw though.
Why did the vector cross the road?
It wanted to be normal.
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#4 2009-04-24 05:10:24
- TheDude
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- Registered: 2007-10-23
- Posts: 361
Re: Determine all solutions
Ahh, good point.
Wrap it in bacon
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#5 2009-04-24 05:39:54
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Determine all solutions
Let me try.
Let
Then the conditions imply
, so we want to solve the cubic equation
By inspection,
is one solution. So we have
If
, two of the roots will be complex. So we want . HenceHopefully, it should be clear that this is the same as
and permutations thereof.Last edited by JaneFairfax (2009-04-24 05:49:36)
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#6 2009-04-24 05:40:59
- tony123
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- Registered: 2007-08-03
- Posts: 229
Re: Determine all solutions
Nice work thanks
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