Math Is Fun Forum

krisper

Member

Registered: 2005-12-20

Posts: 19

Looks simple but actually quite hard

Hi guys,
I have a problem with an equation. Here it is: (x^2 + 4x + 5)/(x+1) = 3√(x+2). I have tried everything but still not getting the roots?! Please help. Thanks.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Looks simple but actually quite hard

Square both sides, mutiply by the denominator, then subtract.  You end up with:

x^4 - x^3 - 10x^2 - 5x + 7 = 0

Which factors into:

(x^2 + x - 1)(x^2 - 2x - 7) = 0

And you use the quadratic from there.  It comes out to (-√5 + 1)/2, (√5- 1)/2, -2√2 + 1, and 2√2 - 1.

Last edited by Ricky (2006-01-15 02:39:32)

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Looks simple but actually quite hard

How on earth did you manage to factor that?
Was it trial and error, or was there some obscure method that I haven't heard of?

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Looks simple but actually quite hard

I'm just that good.

Nah, I used a ti-89.  It uses some fairly complex algorithms to do it, most of which would be unusable by a human.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

krisper

Member

Registered: 2005-12-20

Posts: 19

Re: Looks simple but actually quite hard

Ricky,

Can you show us the algorithm that is being used or write here how  x^4 - x^3 - 10x^2 - 5x + 7 = 0 is being factored as it is very important for me to understand it. Thanks.

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Humankind's inherent sense of right and wrong cannot be biologically explained.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Looks simple but actually quite hard

Boy, if only I could.  But Texas Instruments protects stuff like that.

But it isn't krisper.  Factoring a quartic equation is only an exercise if you are bored or insane.  No math teacher woudl ever have you do this, nor would you learn anything from doing it.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Looks simple but actually quite hard

We must solve the system
cd=7
a+b=-1
ab+d+c=-10

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IPBLE:  Increasing Performance By Lowering Expectations.

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Looks simple but actually quite hard

And one more condition:
ad+bc=-5

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IPBLE:  Increasing Performance By Lowering Expectations.