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Quadratic surfaces question

  1. Oct 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Write the following quardatic surface equation as a sum of multiples of
    squares of independent linear functions

    [itex]x^{2}+4y^{2}+56z^{2}+2xy+4xz+28yz[/itex]

    2. Relevant equations



    3. The attempt at a solution

    Please see attachment.

    nb. there is no answer provided by the tute, but from all the previous exercises, it should
    be in the form of something like [itex](ax + by -cz)^{2} + (dx + ey -fz)^{2} + g^{2}[/itex]


    My problem is that I have no effective and quick way to solve these sorts of problems using the complete the squares method.

    I would have to spend hours trying to find a combination that will make the equation balance out
     

    Attached Files:

  2. jcsd
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