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Inequality Proof

  1. Jun 29, 2010 #1
    1. The problem statement, all variables and given/known data

    If |x-1| < 1 then Prove |x^2 -4x + 3| < 3.

    2. Relevant equations

    3. The attempt at a solution

    proof: Assume |x-1| < 1. Then X has to be between 0 and 2.Because X has to be between 0 and 2 then |x-3|<3,and |x-1||x-3|<3 by multiplication of inequalities.
    |x-1||x-3|=|x^2 - 4x + 3| by distribution. Thus, |x^2 -4x + 3| < 3. (QED)

    I was wondering if this is sufficient. I was a little unsure if what I did in the second sentence, and the start of the third was ok

    Thank you.
  2. jcsd
  3. Jun 29, 2010 #2


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    Science Advisor

    Yes, that is exactly right!
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