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

ganesh
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Registered: 2005-06-28
Posts: 15,169

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?


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

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

Re: Algebra

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


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

Re: Algebra

good%20job.gif


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

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

Re: Algebra

Thanks.


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

Re: Algebra

A # 2

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


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

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

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: 15,169

Re: Algebra

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


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

Re: Algebra

A # 4

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


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

Re: Algebra

Well done, mathsyperson! up


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

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.


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

ganesh
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Registered: 2005-06-28
Posts: 15,169

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


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

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,169

Re: Algebra

A # 7

Solve: (x²+1/x²) - 3(x-1/x)-2=0


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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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,672

Re: Algebra

Hi ganesh;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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: 15,169

Re: Algebra

Hi soroban,

I too get the same solutions. Well done!


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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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