Inequality Proof

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Homework Statement



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


Homework Equations





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.
 

Answers and Replies

  • #2
HallsofIvy
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Yes, that is exactly right!
 

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