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#1 2006-04-06 02:28:15
- krassi_holmz
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a b + c d = 6 && a c - 3 b d = 5
Find all integer solutions of the system:
a b + c d = 6 && a c - 3b d = 5.
IPBLE: Increasing Performance By Lowering Expectations.
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#2 2006-04-06 13:16:56
- George,Y
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Re: a b + c d = 6 && a c - 3 b d = 5
(a+d)(b+c) = 6+5+4bd
X'(y-Xβ)=0
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#3 2006-04-06 14:02:30
- mikau
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Re: a b + c d = 6 && a c - 3 b d = 5
thats the solution?
A logarithm is just a misspelled algorithm.
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#4 2006-04-06 20:18:09
- krassi_holmz
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Re: a b + c d = 6 && a c - 3 b d = 5
:0
No. You haveto find all fours (a0,b0,c0,d0) elem Z:
a0 b0 + c0 d0 = 6 && a0 c0 - 3 b0 d0 = 5
IPBLE: Increasing Performance By Lowering Expectations.
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#5 2006-04-07 03:13:47
- George,Y
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Re: a b + c d = 6 && a c - 3 b d = 5
(a+d)(b+c) = 6+5+4bd
contains all the information of a b + c d = 6 and a c - 3b d = 5. and it might be a path. i'm new in this field, and what i could do is shifting, to see if it has been made simplier....
Last edited by George,Y (2006-04-07 03:15:54)
X'(y-Xβ)=0
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#6 2006-04-07 05:33:42
- krassi_holmz
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Re: a b + c d = 6 && a c - 3 b d = 5
You are not so right:
{a b + c d = 6 && a c - 3b d = 5} => {(a+d)(b+c) = 11+4bd}, but:
{a b + c d = 6 && a c - 3b d = 5} !<=> {(a+d)(b+c) = 11+4bd}, so not all solutions of your equation will be solutions to the system.
IPBLE: Increasing Performance By Lowering Expectations.
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#7 2006-04-07 20:07:00
- George,Y
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Re: a b + c d = 6 && a c - 3 b d = 5
yes, you'r right. sufficient but not necessary. at least one of the original equation have to be contained.
from a c - 3b d = 5, ac-5 contain 3 , ac elem {8,11,14...}
X'(y-Xβ)=0
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#8 2006-04-08 22:10:24
- krassi_holmz
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Re: a b + c d = 6 && a c - 3 b d = 5
a c elem {...8,11,14,...}:: a IS integer
IPBLE: Increasing Performance By Lowering Expectations.
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