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

Solve in positive integers the cubic

x^3–(x+1)^2=2001

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

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, there has to be a point!

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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

The knowledge of some things as a function of age is a delta function.

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