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Square both sides inequality help

  1. Jun 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove: xyzw[tex]\geq x+y+z+w-3[/tex],where [tex]x\geq 1,y\geq 1,z\geq 1,w\geq 1[/tex]

    2. Relevant equations

    3. The attempt at a solution

    The only thing i could try is to square both sides but then this leads nowhere.

    Any ideas??
  2. jcsd
  3. Jun 13, 2010 #2
    Re: inequality

    Start with the following inequalities: (Why are they true?)

    0 ≤ (xy-1)(zw-1)
    0 ≤ (x-1)(y-1)
    0 ≤ (z-1)(w-1)​
  4. Jun 14, 2010 #3
    Re: inequality

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