Results 1 to 3 of 3

Math Help - Urgent How Do U Find The Inequality For This

  1. #1
    Newbie
    Joined
    Jun 2007
    Posts
    18

    Urgent How Do U Find The Inequality For This

    i don't get how to do this cause i dunt think you can factor it

    how do u solve this inequality

    x^3+3x^2-18x < and equal to 22
    ???????????????????????????????
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by calchelp View Post
    i don't get how to do this cause i dunt think you can factor it

    how do u solve this inequality

    x^3+3x^2-18x < and equal to 22
    ???????????????????????????????

    Well x^3+3x^2-18x-22=0 has three real roots but none of them are "nice".

    Depending on the context I would be tempted to sketch the curve y=x^3+3x^2-18x-22 to obtain the approximate roots, and identify the relevant regions where x^3+3x^2-18x\le 22

    RonL
    Attached Thumbnails Attached Thumbnails Urgent How Do U Find The Inequality For This-gash.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by calchelp View Post
    i don't get how to do this cause i dunt think you can factor it

    how do u solve this inequality

    x^3+3x^2-18x < and equal to 22
    ???????????????????????????????
    Hello,

    you asked this question already. I couldn't get a simple solution and I can only show you how to get some approximations:

    1. x^3+3x^2-18x \leq 22 you only can factor the LHS of this inequality:
    x(x-3)(x+6) \leq 22 but I don't know how to use this "result".

    2. What I did:
    Consider the function:
    f(x) = x^3+3x^2-18x-22

    Calculate the zeros of f by the Newton method. I got:
    x_1 = -5.534193... \vee x_2 = -1.095279... \vee x_3 = 3.629472... Using these values to 2 sign. digits you can factor the term f(x) into:
    f(x) \approx (x+5.53)(x+1.10)(x-3.63)

    Now calculate f(x) \leq 0
    A product of 3 factors is negative (that's the same as lower zero) if 2 factors have the same sign and one factor is negative. Thus you'll get a system of linear inequalities:
    f(x) \leq 0 \Longrightarrow

    x+5.53\geq 0 \wedge x+1.1\geq  0 \wedge x-3.63 \leq 0 \; \; \; \vee

    x+5.53\leq 0 \wedge x+1.1 \leq 0 \wedge x-3.63 \leq 0 \; \; \; \vee

    x+5.53\geq 0 \wedge x+1.1 \leq 0 \wedge x-3.63\geq  0\; \; \;  \vee

    x+5.53 \leq 0 \wedge x+1.1 \geq 0 \wedge x-3.63 \geq 0

    Now solve these inequalities for x. The final result should be:
    x \leq -5.53 \; \vee \; -1.1 \leq x \leq 3.63

    I've attached diagrams of the graph of g(x)=f(x)+22=x^3+3x^2-18x and y = 22. Those parts of the graph which are below y = 22 are marked in green or red.
    Attached Thumbnails Attached Thumbnails Urgent How Do U Find The Inequality For This-unglg_drittgrad.gif  
    Last edited by earboth; June 23rd 2007 at 10:31 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the congruence, urgent please
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: May 11th 2009, 05:18 PM
  2. Urgent Inequality Help Please
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 12th 2007, 03:33 PM
  3. Replies: 2
    Last Post: September 9th 2007, 07:13 AM
  4. Find The Y Intercept - Urgent
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 25th 2007, 08:29 PM
  5. Urgent and important??! integral inequality
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 17th 2006, 03:05 PM

Search Tags


/mathhelpforum @mathhelpforum