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Math Help - Equations problem

  1. #1
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    Equations problem

    HI! Actually I have no idea of how to solve this problem, could any one help me please? You have to find de values for A, B and C.
    Equations problem-problemeq.png
    Thanks
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  2. #2
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    You have

    \begin{cases}x + y + z = 3 \\ x^2 + y^2 + z^2 = 9 \\ xyz = -2\end{cases}

    From equation 1:

    x = 3 - y - z, so


    \begin{cases}(3 - y - z)^2 + y^2 + z^2 = 9\\ (3 - y - z)yz = -2\end{cases}

    \begin{cases}(3 - y - z)^2 + y^2 + z^2 = 9 \\ zy^2 + (z^2 - 3z)y - 2 = 0\end{cases}

    Since the final equation is now a quadratic in y, you can solve for y in terms of z using the quadratic formula.

    Everything else should piece together after that.
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