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Math Help - Algebraic Problem Need Solve Urgent

  1. #1
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    Algebraic Problem Need Solve Urgent

    I am bothered with a problem to solve the equation


    a3+b3 = 91
    a2+b2=61


    find the value of and "a" and "b".

    where 3 and two is in form of cube and square



    Please help me to solve this problem
    Last edited by gautam; June 18th 2008 at 10:13 PM. Reason: Just to Set acutal placement of 2 and 3
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by gautam View Post
    I am bothered with a problem to solve the equation


    a<sup>3</sup>+b<sup>3</sup> = 91
    a<sup>2</sup>+b<sup>2</sup>= 61


    find the value of and "a" and "b".



    Please help me to solve this problem
    If you mean a^3 + b^3 = 91, a^2 + b^2 = 61, Are a and b integers? Or are they real numbers?

    By trial and error you can get one set though: a = -5 and b = 6
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  3. #3
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    Quote Originally Posted by gautam View Post
    I am bothered with a problem to solve the equation


    a3+b3 = 91
    a2+b2=61


    find the value of and "a" and "b".

    where 3 and two is in form of cube and square



    Please help me to solve this problem




    Thanks for find the values but i need complete method if you can please help me
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  4. #4
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    Quote Originally Posted by gautam View Post
    Thanks for find the values but i need complete method if you can please help me
    put u=a+b and v=ab, then the equations become:

    u^2-2v=61

    u^3-3uv=91

    or:

    u^2=61+2v

    u^3=91+3uv

    Dividing gives:

    u=\frac{91+3uv}{61+2v}

    rearranging:

     <br />
v=\frac{61u-91}{u}<br />

    Now substitute this back into u^2-2v=61 to get:

    u^2-2\frac{61u-91}{u}=61

    Which is a cubic in u, solve this, then use these solutions to find the corresponding v's and so the a's and b's. (solution of the cubic will be eased by using Isomorphism's result).

    RonL
    Last edited by CaptainBlack; June 19th 2008 at 05:01 AM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by gautam View Post
    I am bothered with a problem to solve the equation


    a3+b3 = 91
    a2+b2=61


    find the value of and "a" and "b".

    where 3 and two is in form of cube and square



    Please help me to solve this problem
    You could start by sketching the curves, see attachment.

    RonL
    Attached Thumbnails Attached Thumbnails Algebraic Problem Need Solve Urgent-gash.jpg  
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  6. #6
    GAMMA Mathematics
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    I just wanted to mention that those two solutions posted by Captain Black were excellent.
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