Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2006-04-06 02:28:15

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

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.

Offline

#2 2006-04-06 13:16:56

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

Re: a b + c d = 6 && a c - 3 b d = 5

(a+d)(b+c) = 6+5+4bd


X'(y-Xβ)=0

Offline

#3 2006-04-06 14:02:30

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

Re: a b + c d = 6 && a c - 3 b d = 5

thats the solution?


A logarithm is just a misspelled algorithm.

Offline

#4 2006-04-06 20:18:09

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

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.

Offline

#5 2006-04-07 03:13:47

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

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....dunno

Last edited by George,Y (2006-04-07 03:15:54)


X'(y-Xβ)=0

Offline

#6 2006-04-07 05:33:42

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

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.

Offline

#7 2006-04-07 20:07:00

George,Y
Member
Registered: 2006-03-12
Posts: 1,306

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

Offline

#8 2006-04-08 22:10:24

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

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.

Offline

Board footer

Powered by FluxBB