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#1 2008-07-01 23:51:02

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

Solve in positive integers the cubic

Solve in positive integers the cubic


x^3–(x+1)^2=2001

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#2 2008-07-02 02:07:19

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

Re: Solve in positive integers the cubic

The solution (obviously) is 13 but you know how Dirty n Untidy n Ugly the cubic equations are to solve!!
If anyone's got a Good way to solve the above, please let me know!!:cool:


If two or more thoughts intersect with each other, then there has to be a point.

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#3 2011-07-28 22:43:45

gAr
Member
Registered: 2011-01-09
Posts: 3,479

Re: Solve in positive integers the cubic

Hi,


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#4 2011-08-02 19:34:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,473

Re: Solve in positive integers the cubic

Hi;

He probably graphed the equation and eyeballed the root as 13. This is an acceptable conjecture which can be proved by plugging in. A little fortuitious but... Then it is trival to prove that it is the only positive root.

You would deflate out the obvious root.

The discriminant of the right side is - 472, so 13 is the only positive root.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2012-05-02 11:35:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Solve in positive integers the cubic

Another way is to use the method developed for solving a general cubic. It is given in a thread of mine and is available on the net.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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