Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Solving a system of equation with a function

I'm wondering if it's possible, but is it possible to solve this System:

with a function?

An example would be

. Solving the cubic

will give you

, in which you can find

where

and

I've been trying for some time, but I don't have the resources such as Mathematica and I don't know if Wolfram Alpha even knows how to do this command.

Last edited by evene (2016-09-19 08:37:45)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

Hi;

With a function? Can you explain?

---

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: Solving a system of equation with a function

I gave an example...

What I meant, is that using a polynomial, can we solve for the unknown values? (by the way,

) are already known.

For the example, you start off with knowing

so you can find

and the cubic. Once you solve the cubic (for

), you can find

by substituting the knowns into

. Giving you

. Using that, you can find

and finish the system.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

What is that right after the equal sign in your cubic?

---

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: Solving a system of equation with a function

A zero.

Do you have any pointers on how to tackle this kind of system of equations? I want to try the same method, but generalize it. Perhaps that could help.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

Hi;

I meant that 2 over that 1.

Since you know a0,a1,a2, and a3 you are left with 4 unknowns and 4 equations. That could be solved using standard methods. Why do you wish to resort to the cubic?

---

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: Solving a system of equation with a function

I just think that it would be easier to have a function that you substitute the knowns into and get the unknowns...

Because right now, it takes a long time to find all the unknowns with the standard method, but substituting everything into a function, you can find one unknown in and find the others really quickly.

Sorry, I still do not understand what you meant by "I meant that 2 over the 1"

It's okay if there isn't a function that can represent this system. I was just wondering. It would make my calculations much easier in the future.

Last edited by evene (2016-09-19 04:05:39)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

This:

Will your four equations always be in the same form?

---

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: Solving a system of equation with a function

Oh... That is an error on my part. It should say

... Sorry!

Yes, no matter what, it will be in that form.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

Then I can maybe convince the mighty M to solve that system in terms of the variables. You would then have a general formula to solve any others. First, you say you will always know what a0, a1, a2, a3 are?

---

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: Solving a system of equation with a function

Who's the Mighty M? Sorry, but I haven't been on the Math is Fun Forum in a while.

Yes, you will always know

for

.

Last edited by evene (2016-09-19 09:26:40)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

M is Mathematica. It can solve your system generically but it is complicated which is to be expected.

The first is for b1

The other 3 are apt to be longer.

---

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: Solving a system of equation with a function

Wow, complicated! Okay, thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

It is like the solution to quartics and cubics. Do you want b0, c1, c0?

---

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: Solving a system of equation with a function

Yeah sure. That would help a lot.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Solving a system of equation with a function

More to come...

---

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.