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Math Help - Inequality Question

  1. #1
    Senior Member Stroodle's Avatar
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    Inequality Question

    What's the best method for solving these without a graph.

    Find \left\{ x:x^{\frac{3}{2}}>x^2 \right\}

    Thanks for your help


    Edit- Oops, wrong thread.
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  2. #2
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    Quote Originally Posted by Stroodle View Post
    What's the best method for solving these without a graph.
    Find \left\{ x:x^{\frac{3}{2}}>x^2 \right\}
    It should be clear to you that x\ge 0 else x^{\frac{3}{2}} is not defined.
    Therefore x^3>x^4.
    Now go for it.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Stroodle View Post
    What's the best method for solving these without a graph.

    Find \left\{ x:x^{\frac{3}{2}}>x^2 \right\}

    Thanks for your help


    Edit- Oops, wrong thread.

    x^{\frac{3}{2}}-x^2>0

     <br />
x^{\frac{3}{2}}(1-x^{\frac{1}{2}})>0<br />

    Draw the number line .
    THus the solution set is { {x: 0<x<1 }}

    Definitely not the best solution .
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    It's clear that both sides are positive, so you can square them, thus x^3>x^4\implies x^2\cdot x(x-1)<0.

    I think you can continue.
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