Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 230

Without use of any calculator

Without use of any calculator, determine

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

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.

tony123

Member

Registered: 2007-08-03

Posts: 230

Re: Without use of any calculator

but from where you get these

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)

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!

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

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
your very last statement:

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igloo myrtilles fourmis

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Re: Without use of any calculator

That's

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

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