1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triangle inequality problem

  1. Sep 16, 2006 #1
    Hello all, I am having some difficulties with a question. Hope you guys can help shine some light on the situation.

    Use the triangle Inequality and the fact that 0< |a| < |b| + => 1/|b| <
    1/|a| to establish the following chains of inequalities.

    |x-2 / x^2+9| "Is less than and equal to" |x| + 2 / 9

    Sorry about the display of the question, I really dont know other way to correctly type it.

    Please explain your answers, and the reason you use such method to answer this question.

    Thanks alot for your much needed help.
  2. jcsd
  3. Sep 17, 2006 #2
    So the triangle inequality is: [tex] |x+y| \leq |x| + |y| [/tex]. We are also given that [tex] 0 < |x| < |y| \rightarrow \frac{1}{|y|} < \frac{1}{|x|} [/tex] and want to establish [tex] |\frac{x^{2}}{x^{2}+9}|\leq \frac{|x|+2}{9} [/tex]
    Last edited: Sep 17, 2006
  4. Sep 17, 2006 #3


    User Avatar
    Science Advisor

    There's a little trick called "parentheses."
  5. Sep 17, 2006 #4
    Thanks for making the question much more understandable.... any help?o:)
  6. Sep 18, 2006 #5
    Please guys need some advice.... Thanks.
  7. Sep 19, 2006 #6
    is it |x-2| or |x^2| /{....} ?
  8. Sep 19, 2006 #7


    User Avatar
    Science Advisor
    Homework Helper

    How big can [itex]x^2/(x^2+9)[/itex] get?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Triangle inequality problem
  1. Triangle Inequality (Replies: 7)

  2. Triangle inequality (Replies: 10)

  3. Triangle inequality (Replies: 2)

  4. Triangle Inequality (Replies: 2)