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Math Help - nice inequality

  1. #1
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    nice inequality

    hi ,

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  2. #2
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    Re: nice inequality

    Quote Originally Posted by abualabed View Post
    hi ,


    Here a graphical solution.
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  3. #3
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    Re: nice inequality

    Abualabed

    since x^2=|x|^2 if you substitute |x| with another variable like t you will get the qubic inequality t^3-2t^2-4t+3<0

    Consider the qubic equation t^3-2t^2-4t+3 =0 and verify that t=3 is a solution . thus factorize the qubic polynomial using Horner's scheme or full division by (t-3) and find t^3-2t^2-4t+3 =(t-3)(t^2+t-1) .
    then solve the equation (t-3)(t^2+t-1) =0 to find the roots it is easy..
    then go back to |x|=t and do the rest ...it is easy.
    your final solution is in the attached figure.
    nice inequality-figure001.png
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  4. #4
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    Re: nice inequality

    Hi,
    Here's a graphical solution as suggested by Plato:

    nice inequality-mhfcalc8.png
    Thanks from abualabed
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