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Math Help - solve - Non-linear System of equations

  1. #1
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    solve - Non-linear System of equations

    solve

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  2. #2
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    Quote Originally Posted by dapore View Post
    solve

    From equation 1:

    x^3 = 3xy^2 + 11

    x^3 - 11 = 3xy^2

    \frac{x^3 - 11}{3x} = y^2

    y = \sqrt{\frac{x^3 - 11}{3x}}.


    Substituting into equation 2:

    y^3 = 3x^2y + 2

    \left(\sqrt{\frac{x^3 - 11}{3x}}\right)^3 = 3x^2\sqrt{\frac{x^3 - 11}{3x}} + 2


    Now try to solve for x.
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  3. #3
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     (1) + i(2) and  (1) - i(2) we have

     (x-iy)^3 = 11+2i ~~ (x+iy)^3 = 11-2i


     x-iy = \sqrt[3]{11+2i} ~~ x+iy = \sqrt[3]{11-2i}


     x = Re(\sqrt[3]{11+2i}) ~~ , ~~ y = - Im(\sqrt[3]{11+2i})
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