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#1 2006-02-26 22:51:50

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Algebra

A # 1

If x² + y² + z² = 50, xy + yz + xz = 47 and xyz = 60,
what is the value of
(i) x
(ii) y and
(iii) (x+y+z)³?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#2 2006-02-27 01:03:01

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Algebra

the numbers are {3,4,5}
12^3=1728


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#3 2006-02-27 01:52:40

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

good%20job.gif


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2006-02-27 03:11:00

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Algebra

Thanks.


IPBLE:  Increasing Performance By Lowering Expectations.

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#5 2006-03-01 04:20:33

ganesh
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Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 2

For waht value of m is 2x³-x²-3mx-24 divisible by x-2?


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#6 2006-03-01 04:40:22

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Algebra

m=2?


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#7 2006-03-01 16:09:19

ganesh
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Registered: 2005-06-28
Posts: 22,992

Re: Algebra

|m|=2 would have been better! The answer is m=-2. Try again, krassi_holmz, probably you made a mistake somewhere.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#8 2006-03-01 16:11:38

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 3

If ax³+bx²+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2), find the values of a and b.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#9 2006-03-01 20:28:39

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 4

The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#10 2006-03-02 04:52:57

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

Re: Algebra

A # 3
From the information given, we can deduce that f(-2) = 0 and f(2) = 4.

-8a + 4b -8 = 0
8a + 4b -4 = 4

Subtract the two equations:
16a -4 = -4
16a = 0
a = 0.

Add the two equations: 8b -12 = 4
8b = 16
b = 2.

f(x) = 2x²+x-6

A # 4
Calling the 2 numbers p and q, we know that p+q = 8, and that 1/p+1/q = 8/15.

Cross-multiplying the second equation gives (p+q)/pq = 8/15. We know that (p+q) = 8, so pq must be 15.

The numbers that add to give 8 and multiply to give 15 are 3 and 5.


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It wanted to be normal.

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#11 2006-03-02 16:26:54

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

Well done, mathsyperson! up


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#12 2006-03-02 17:29:28

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 5

If one of the roots of the equation x²-3x+q=0 is twice the other, find the value of q.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#13 2006-03-06 20:12:43

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 6

If the ratio of the roots of the equation ax²-2ax+b=0 is equal to that of ax²-2cx+d=0, then which of the following is true?

(a) a²b=c²d                                      (b) a²c=b²d

(c) a²d=c²b                                      (d) d²b=c²a


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#14 2006-03-08 16:15:28

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

A # 7

Solve: (x²+1/x²) - 3(x-1/x)-2=0


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#15 2006-03-10 20:09:52

amonjezi
Member
Registered: 2006-03-09
Posts: 9

Re: Algebra

y=4
and,y=-1

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#16 2006-03-10 20:15:51

amonjezi
Member
Registered: 2006-03-09
Posts: 9

Re: Algebra

(x
+1/x^2)-3(x-1/x)-2+2-2=0

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#17 2006-03-10 20:27:02

amonjezi
Member
Registered: 2006-03-09
Posts: 9

Re: Algebra

(x^2+1/x^2)-3(x-1/x)-2+2-2=0  then (x+1/x)^2-3(x-1/x)-4=0    if (x+1/x)=y  y=4 and -1  now we solves (x+1/x)=4 and (x+1/x)=-1     these equaition very easy

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#18 2006-03-11 01:17:49

amonjezi
Member
Registered: 2006-03-09
Posts: 9

Re: Algebra

hi ganesh
choice (a) or(c) are true

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#19 2007-04-23 08:20:02

Eeyore
Member
Registered: 2007-04-16
Posts: 8

Re: Algebra

a7   1 and -1

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#20 2007-04-23 08:41:04

Eeyore
Member
Registered: 2007-04-16
Posts: 8

Re: Algebra

A#5   q=2

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#21 2010-10-22 00:12:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,535

Re: Algebra

Hi ganesh;


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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#22 2011-02-12 07:37:00

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Algebra


. .


.

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#23 2011-02-12 07:58:53

soroban
Member
Registered: 2007-03-09
Posts: 452

Re: Algebra



.

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#24 2011-02-13 01:06:44

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,992

Re: Algebra

Hi soroban,

I too get the same solutions. Well done!


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#25 2011-03-02 05:54:20

G-man
Member
Registered: 2011-02-28
Posts: 16

Re: Algebra


Maths!......sleep

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