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#1 2006-02-06 08:59:50

RauLiTo
Member
Registered: 2006-01-11
Posts: 142

equation number 2

try to get X smile :

[ X - 1 / X ] ³ + 3 [ X - 1 / X ] + 30 = 0
X = ?

it look easy but i don't know whats wrong with this mind eek


ImPo$$!BLe = NoTH!nG
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#2 2006-02-06 10:37:43

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

Re: equation number 2

I think the best way of doing this would be to solve y³ + 3y + 30 = 0, then use that answer to solve y = x-1/x.

Unfortunately, I have no idea how to solve cubic equations. But hopefully I've put you on the right track.


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

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#3 2006-02-06 11:29:37

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: equation number 2

Here's my stab.

I took your equation and expanded it to;

(x^6 + 30x - 1) / x^3 = 0  ( I don't feel like typing out the steps, I'm sure you can do it too.)

So this only equals zero if;

x^6 + 30x - 1 = 0

Let x^3 = y,  then;

y^2 + 30y - 1 = 0

Using the quadratic equation gives;

y = .033296378.. and -30.03329638...

Since y = x^3,  x = y^1/3

x = .321710818... and -3.1081632...


edit*

   I checked this with my TI-89 and my answer was confirmed correct.  The slight error from being exact is only from rounding the value of x.

   The precise answer is;

  -(√(226) + 15)^(1/3)  and  (√(226) - 15)^(1/3)

   Which agrees with what I had earlier.

   We don' need no stinkin' calculators....

Last edited by irspow (2006-02-06 13:05:40)

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#4 2006-02-06 19:08:01

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

Re: equation number 2

Right.
Actually there are several more complex roots:






Last edited by krassi_holmz (2006-02-06 19:14:31)


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#5 2006-02-06 21:03:13

kempos
Member
Registered: 2006-01-07
Posts: 77

Re: equation number 2

i don't get this step:

x^6 + 30x - 1 = 0

Let x^3 = y,  then;

y^2 + 30y - 1 = 0

why do you have 30y if y = x^3?

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#6 2006-02-06 21:13:02

RauLiTo
Member
Registered: 2006-01-11
Posts: 142

Re: equation number 2

thanks everybody for helping as kempos said i dind't get that one


ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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#7 2006-02-06 21:14:10

RauLiTo
Member
Registered: 2006-01-11
Posts: 142

Re: equation number 2

krassi_holmz ... i want the way you get the answer please man


ImPo$$!BLe = NoTH!nG
Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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#8 2006-02-06 21:41:17

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

Re: equation number 2

I used Mathematica.
Must write something like this:
Solve[( X - 1 / X ) ³ + 3 ( X - 1 / X ) + 30 == 0,X]


IPBLE:  Increasing Performance By Lowering Expectations.

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#9 2006-02-07 08:23:00

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: equation number 2

Sorry guys, it was a typing mistake. The "30x" should have been 30x^3.  I didn't even noticed that I typed it that way.  If I actually used the 30x, I would have never have gotten the answer.
Sorry, again.

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