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Math Help - Finding all r ∈ R such that r<1+1/r?

  1. #1
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    Finding all r ∈ R such that r<1+1/r?

    Find all r ∈ R such that r<1+1/r?
    So I'm having difficulty with this problem.
    I've figured out that r is a variable and r does not = 0 and by solving it, multiplying both sides by r is incorrect.

    Can you guys help me with this problem?
    My first instinct is to just multiply both sides by r but that's apparently wrong.

    Any help is appreciated.

    I got some help elsewhere. Thanks though.
    Last edited by paperclip5; December 18th 2011 at 05:30 PM. Reason: Solved
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  2. #2
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    Re: Finding all r ∈ R such that r<1+1/r?

    Quote Originally Posted by paperclip5 View Post
    Find all r ∈ R such that r<1+1/r?
    So I'm having difficulty with this problem.
    I've figured out that r is a variable and r does not = 0 and by solving it, multiplying both sides by r is incorrect.

    Can you guys help me with this problem?
    My first instinct is to just multiply both sides by r but that's apparently wrong.

    Any help is appreciated.

    I got some help elsewhere. Thanks though.
    It's not that multiplying both sides by r is wrong- you just have to be careful. If you multiply both sides of an inequality by a negative number, you reverse the direction of the inequality.

    Yes, as you say, r cannot be 0- so it is either positive or negative. If it is positive, multiplying both sides by r gives r^2< r+ 1 which is the same as r^2- r- 1< 0. If r is negative, multiplying both sides by r gives r^2> r+ 1 which is the same as r^2- r- 1> 0. Obviously, determining where r^2- r- 1= 0 is important in solving those! Don't forget that the first is only true for r> 0 and the second for r< 0.
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