Math Is Fun Forum

Oh, right. I am looking for integer solutions.

Yeah, I understand how to do the problem. The fruit salad question was easy. Just add up and divide by the 2 quarts you have to get 3/8.

Oh... But do you know what are the two Quartics? Wolfram Alpha isn't capable of understanding my input, for some weird reason. Really wish I had Mathematica.

Yeah sure. That would help a lot.

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

.

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.

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.

Substituting

with

unfortunately does not work. But perhaps you have to substitute

with something different, such as

and then substitute

with something else... Just a thought.

I wonder if Vieta's Trigonometric Solution will work for this... It should. But it may not give me the answer in the format that I would like...

Wait, Bobbym, can you use your ISC thing to compute the roots of

? Setting

does not work.

Okay, that works too!

...

I substituted

to get

We want the roots, so setting

will give us the roots.