1. Not finding help here? Sign up for a free 30min 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!

Proof: |A - B | <

  1. Sep 20, 2004 #1
    There are many questions i can't get. This is just one. Can anyone give me a hint on what to do? It's probably really simple :(

    If A and B are real numbers such that [tex]|A - B| < \frac{1}{2}[/tex], show that:

    [tex]|A^2 - B^2| \leq \frac{1}{2} \{2|B|+
    \frac{1}{2} \}[/tex]
     
    Last edited: Sep 20, 2004
  2. jcsd
  3. Sep 20, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Welcome to PF!
    Try to rewrite [tex]|A^{2}-B^{2}|[/tex] as a product of two expressions..
    (It's a well known identity)
     
  4. Sep 20, 2004 #3
    Is this what you meant?

    [tex] |(A+B) (A-B)| \leq |B| + \frac{1}{4} [/tex]

    If so, i already had that but didn't know where to go from there...already wasted a lot of paper going no where :grumpy:

    Am i supposed to use [tex] -\frac{1}{2} < A - B < \frac{1}{2} [/tex] somewhere?

    thanks
     
    Last edited: Sep 20, 2004
  5. Sep 20, 2004 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    First of all:
    You are to PROVE that inequality, not ASSUME it!!
    Hence, what you start with, is the following EQUALITY:
    [tex]|A^{2}-B^{2}|=|A-B||A+B|[/tex]
    (Ok so far?)
    Now, use the inequality you've been given to derive:
    [tex]|A^{2}-B^{2}|=|A-B||A+B|\leq\frac{1}{2}|A+B|[/tex]
    Agreed?
    Now you'll need to use your given inequality to provide an estimate of |A+B|!
     
  6. Sep 20, 2004 #5

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    PS:
    You'll need to use the triangle inequality as well..
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Proof: |A - B | <
  1. Proof required (Replies: 6)

  2. Direct Proof (Replies: 1)

  3. Problem with Proof (Replies: 3)

  4. Intro to proofs (Replies: 6)

  5. Proof help (Replies: 1)

Loading...