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Thread: solving for X

  1. #1 solving for X 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Okay, i know that there is a general form of the solution to a polynomial with n=3. Now say the equation stated below:



    could we solve this as if it were:



    would appreciate any reasonable answer


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  3. #2  
    Forum Bachelors Degree x(x-y)'s Avatar
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    I don't see why you couldn't express it like that, you're basically just using a disguised quadratic of

    Let x = sin10.


    "Nature doesn't care what we call it, she just does it anyway" - R. Feynman
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  4. #3 Re: solving for X 
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    Quote Originally Posted by Heinsbergrelatz
    Okay, i know that there is a general form of the solution to a polynomial with n=3. Now say the equation stated below:



    could we solve this as if it were:



    would appreciate any reasonable answer
    In your original equation you have only constants (sin10, sin30, etc.). What are you solving for?
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  5. #4  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    iu am trying to solve for sin10, yea i know sin10 seems like a constant, but my idea is trying to pretend sin10 as some "x" so i can solve the cubic equation, and my question is are we allowed to do this?? because i have tried and i get answers with complex numbers in it..

    then i ask myself a question, WHAT DOES THE IMAGINARY UNIT IN SURDS OF TRIG. ANGLES ACTUALLY REPRESENT??
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  6. #5  
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    If you mean 10 is x and 30 is 3x, then the equation involves sinx and sin3x. The practical way to solve such equations is to form f(x) = 0, determine the derivative of f(x), say f'(x) and then use Newton-Raphton to find solutions with randomly or judgementally chosen starting estimates for x based on a graphing software. This is a simple problem if you know/have a course in Numerical Analysis and access to spreadsheet software.
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  7. #6  
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    Quote Originally Posted by Heinsbergrelatz
    iu am trying to solve for sin10, yea i know sin10 seems like a constant, but my idea is trying to pretend sin10 as some "x" so i can solve the cubic equation, and my question is are we allowed to do this?? because i have tried and i get answers with complex numbers in it..

    then i ask myself a question, WHAT DOES THE IMAGINARY UNIT IN SURDS OF TRIG. ANGLES ACTUALLY REPRESENT??
    A cubic equation must have at least one real root.
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