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Proof in simple Algebra

  1. Mar 28, 2005 #1
    Hi,

    I need to prove that for every a > 1 and b > 1 the following holds:

    ab - a - b + 2 > 1

    Can someone please throw me some hints? :)

    Thanks,
    Chen
     
  2. jcsd
  3. Mar 28, 2005 #2
    It's equivalent to proving

    ab - a - b + 1 > 0
    <=>
    a(b - 1) - b + 1 > 0
    <=>
    -a(b - 1) + b - 1 < 0
    <=>
    (b - 1)(1 - a) < 0.
     
  4. Mar 28, 2005 #3
    Argh, I was close but didn't see that! Thanks. :-)
     
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