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

try to get X :

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

X = ?

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

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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

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

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

Right.

Actually there are several more complex roots:

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

IPBLE: Increasing Performance By Lowering Expectations.

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

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

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

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

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

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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