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How to derive inequalities

  1. May 28, 2009 #1

    thrill3rnit3

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    Gold Member

    1. The problem statement, all variables and given/known data

    Derive the following inequality.

    2. Relevant equations

    x[tex]^{2}[/tex]+xy+y[tex]^{2}[/tex] [tex]\geq[/tex] 0

    3. The attempt at a solution

    I don't know how to get started. How do you derive inequalities?

    I'm not looking for the answer, just general tips.
     
    Last edited: May 28, 2009
  2. jcsd
  3. May 28, 2009 #2

    danago

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    That term on the left looks similar to (x+y)(x+y). How could you use that?
     
  4. May 28, 2009 #3

    thrill3rnit3

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    (x+y) squared has +2xy as its middle term
     
  5. May 29, 2009 #4

    Mark44

    Staff: Mentor

    I don't think the similarity (or not) to (x + y)(x + y) is any help.

    Think about the equation x2 + xy + y2 = 0.
    Are there any real solutions to this equation?

    If yes, then the real solutions (x, y) are the graph of a curve that separates the portion of the plane for which x2 + xy + y2 > 0 from the other portion of the plane where x2 + xy + y2 < 0.

    If no, then all points (x, y) in the plane must satisfy exactly one of the inequalities listed in the previous paragraph.
     
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