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## #1 2008-07-18 09:47:54

tony123
Member
Registered: 2007-08-03
Posts: 189

### Without use of any calculator

Without use of any calculator, determine

Last edited by tony123 (2008-07-18 09:48:53)

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## #2 2008-07-24 23:39:43

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Without use of any calculator

,
, and
all satisfy the equation
. Try and play around with that.

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## #3 2008-07-24 23:58:11

tony123
Member
Registered: 2007-08-03
Posts: 189

### Re: Without use of any calculator

but from where you get these

JaneFairfax wrote:

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## #4 2008-07-25 01:25:33

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Without use of any calculator

Never mind, forget what I wrote above. I was being naughty and used a calculator.

But I got it now. Heres how.

By considering the sum of the complex roots of

, you have

But

.

Now

Note that

. Hence

And

. And there you have it.

Last edited by JaneFairfax (2008-07-25 01:27:41)

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## #5 2008-07-25 03:26:26

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

### Re: Without use of any calculator

Kya baat hai!!?
That's a nice smiley too by the way!

If two or more thoughts intersect, there has to be a point!

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## #6 2008-07-25 20:19:53

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Without use of any calculator

Jane, I don't get where the cube is coming from in

igloo myrtilles fourmis

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## #7 2008-07-25 20:26:04

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

### Re: Without use of any calculator

That's

If two or more thoughts intersect, there has to be a point!

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## #8 2008-07-25 23:54:41

Identity
Member
Registered: 2007-04-18
Posts: 934

### Re: Without use of any calculator

Can't wait till I learn complex numbers, it looks so useful

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