Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

What condition makes this equation true?

I have the following equation

And I need a condition for them to be equal. So my problem is: What is that condition?

Please no trivial answers please.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What condition makes this equation true?

Usually non-trivial means m,n,s,t ≠ 0. Any other restrictions on m,n,s,t?

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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.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: What condition makes this equation true?

Yes, m,n,s,t ≠ 0. And you cannot just restate the problem.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What condition makes this equation true?

If I get it you will not have to worry about that, I do not know what restate the problem means...

---

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.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: What condition makes this equation true?

Like, you can't simply say

"The equation is satisfied when

"

Because.... well... that's obvious... right?

I'm just looking for simpler cases when both sides are equal.

Last edited by evene (2016-11-05 09:35:34)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What condition makes this equation true?

Do you not have to solve for the variables to do that?

---

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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: What condition makes this equation true?

It would help if you provided some background for where this equation came from. A polynomial in 4 variables of degree 6 is not going to be easy to find constraints on, in general.

An obvious solution is m = n = s = t = 1, and you can probably find others quite easily by setting some subset of {m,n,s,t} equal to ±1. Or just set any three of m,n,s,t equal to whatever values you like and solve for the remaining variable. (There will of course be infinitely many solutions if you want to solve over the complex numbers.)

Last edited by zetafunc (2016-11-05 09:45:52)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What condition makes this equation true?

So far, I have not heard of any constraints at all. Are they integers, Positive integers, Reals?

---

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.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: What condition makes this equation true?

No, you don't have to explicitly solve for m. I just added that, because I thought that solving for m would help find the actual constraint.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: What condition makes this equation true?

Probably m=n=1 and t=1 may be the minimum restraints to make them equal,unless it is considered trivial.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

evene

Member

Registered: 2015-10-18

Posts: 272

Re: What condition makes this equation true?

But I don't need values for m,n,s,t. I just want to simplify the above equation...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: What condition makes this equation true?

Hi;

Simplify? In what sense?

---

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.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: What condition makes this equation true?

Like... reduce the equation to another equation.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: What condition makes this equation true?

It would help if you provided some background for where this polynomial came from, or why you want to find its solution set.