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Thread: Combining two equations by addition or multiplication?

  1. #1
    Apr 2010

    Combining two equations by addition or multiplication?

    Hello all,

    I have a seemingly simple question concerning the combination of two quadratic equations:

    z(x) = x^2 + 2*x - 1

    z(y) = 2*y^2 + 3*y + 1

    What is the significance of combining these two equations by multiplying them together versus simply adding them together? I know if I take the product of the two equations, I will end up with a 2D surface described by equation z(x,y). But what is the difference between that and the equation obtained by adding them together, z(x,y)?

    Any insight on this will be much appreciated.

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  2. #2
    MHF Contributor
    Aug 2007
    Your question is one of degree only.
    • Add quadratic to quadratic to get some other quadratic surface.
    • Multiply quadratic by quadratic to get a quartic surface of some sort.
    The actual meaning of the act would depend on your application.
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