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Math Help - Find a Fixed Cubic

  1. #1
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    Find a Fixed Cubic

    I am working on a problem, the remaining step I need to do is very computational.
    I am mathematically software challenged, can some one find the solution to this problem:

    Find a,b,c,d,e,f,g,h (real numbers) and with a,e\not = 0 so that if in the function f(x) = \tfrac{ax^3+bx^2+cx+d}{ex^3+fx^2+gx+h} we replace x by \tfrac{ - x - \sqrt{3}}{\sqrt{3}x-1} then we end up with the same function, i.e. f(x) = f\left( \tfrac{-x-\sqrt{3}}{\sqrt{3}x-1} \right).
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  2. #2
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    Take a look at this. I think I understand your question. I'm holding x as 1 for both sides. I take the value of the 2nd function using x=1, and then plug that in as the x value to the main F(x). Do you want me to write something to loop through a-h to find your target values?
    Attached Files Attached Files
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  3. #3
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    Thank you, but like I said I am mathematically software challenged I do not even have Excel.
    Can you PrintScreen your answer?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Thank you, but like I said I am mathematically software challenged I do not even have Excel.
    Can you PrintScreen your answer?
    It says
    a=-1
    b=-20
    c=-30
    d=-243
    e=-2
    f=6
    h=8
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  5. #5
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    Quote Originally Posted by Mathstud28 View Post
    It says
    a=-1
    b=-20
    c=-30
    d=-243
    e=-2
    f=6
    h=8
    Okay I will try that. Can you check that, if you have computer-algebra system on your computer. I am too lazy to.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Okay I will try that. Can you check that, if you have computer-algebra system on your computer. I am too lazy to.
    I don't, I'm sorry
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  7. #7
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    I just tried graphing this function and it does not work.
    I used g=0, because you never told me what value is, I assumed it was zero.
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  8. #8
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    Sorry gentleman, I should have described better. The numbers on that file are starting points, not the answer.

    My question to you was do you want me to set x = 1 for both equations. After that, my thought was run my program to come up with a combination for each to match equations.

    If that's what you want, I'll program that.
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  9. #9
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    Quote Originally Posted by mathceleb View Post
    If that's what you want, I'll program that.
    I am looking for coefficients that when I substitute the linear rational function and after simplifying denominator and all that stuff I end up with the same expression as I started. So it seems this is a linear algebra problem with 8 variables.
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  10. #10
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    Quote Originally Posted by ThePerfectHacker View Post
    I am looking for coefficients that when I substitute the linear rational function and after simplifying denominator and all that stuff I end up with the same expression as I started. So it seems this is a linear algebra problem with 8 variables.
    Ok, that makes sense. Let me take a look and see if I can code this for you. My "day job" is really busy this week, so I'll see what I can do this week after hours.
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  11. #11
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    Thank you, but like I said I am mathematically software challenged I do not even have Excel.
    Can you PrintScreen your answer?
    Here is the screen capture. As we see with these coefficients the right side does not equal the right side, they are only an example.

    RonL
    Attached Thumbnails Attached Thumbnails Find a Fixed Cubic-gash.jpg  
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  12. #12
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    Thank you for the function, but the problem got solved a few days ago. I should have posted on this thread the answer but I forgot to.
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  13. #13
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    Quote Originally Posted by ThePerfectHacker View Post
    Thank you for the function, but the problem got solved a few days ago. I should have posted on this thread the answer but I forgot to.
    Oh, great news! I'll cease work on this then.
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