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Quick Inequality Question

  1. Mar 18, 2009 #1
    I first accidentally posted this in Calculus & Beyond since it is for a 700-level class, but I'm realizing now that it's pretty basic, and it should probably go here:

    I'm working on a problem in which I have to find a range for r. I have an upper bound on it, but I can't seem to get the lower bound.

    Here is the inequality to start with:
    [tex]\lambda[/tex]r - r3 + [tex]\lambda[/tex] < 0

    Eventually, I get it down to:
    [tex]\lambda[/tex] < [tex]\frac{r^3}{r+1}[/tex]

    However, I need r by itself on one side, and I have no idea what to do. Is there anything I actually could do or am I stuck?

    Another note: r>0 and [tex]\lambda[/tex]>0. Thanks!
  2. jcsd
  3. Mar 18, 2009 #2


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    You can't in any simple way. You can use the fact that points where one side is equal separate "<" from ">". However you still need to solve [itex]r^3- \lamba r- \lambda= 0[/itex]. There is a "cubic formula" but it is very complicated.
  4. Mar 18, 2009 #3
    Okay, yeah, I've worked with the cubic formula in undergrad, but I very highly doubt we're expected to be using it here. I'll have to check with my teacher tomorrow, thanks so much!
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