Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

Solve in positive integers the cubic

Solve in positive integers the cubic

x^3–(x+1)^2=2001

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:

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gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Solve in positive integers the cubic

Hi,

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

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