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Math Help - Inequality with higher degree

  1. #1
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    Inequality with higher degree

    x^4-x<0

    How do I solve it?
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  2. #2
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    Re: Inequality with higher degree

    Have you tried to factor the LHS yet?
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  3. #3
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    Re: Inequality with higher degree

    I tried doing X(X^3 -1) <0 then x=0 x^3-1=0 didn't work when i checked using solution
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    Re: Inequality with higher degree

    Maybe you can factor \displaystyle x^3-1 further?

    Hint: \displaystyle a^3-b^3 = (a-b)(a^2-ab+b^2)

    Sketching the graph of f(x) = x^4-x will help after you have found the zeros.
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  5. #5
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    Re: Inequality with higher degree

    Quote Originally Posted by RK29 View Post
    x^4-x<0 How do I solve it?
    Can you see that x\not= 0~?
    So can you solve x^3-1<0~?
    If so solve it.
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  6. #6
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    Re: Inequality with higher degree

    Quote Originally Posted by RK29 View Post
    I tried doing X(X^3 -1) <0 then x=0 x^3-1=0 didn't work when i checked using solution
    Hint: f(1)=0 and so (x-1) is a factor.
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    Re: Inequality with higher degree

    Quote Originally Posted by RK29 View Post
    x^4-x<0

    How do I solve it?
    x^4 is non-negative number for all  x\in\mathbb{R}

    So when, x^4<x ?

    x must be positive, but not greater than 1. Can you see that?
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  8. #8
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    Re: Inequality with higher degree

    Quote Originally Posted by RK29 View Post
    x^4-x<0

    How do I solve it?
    x^4 - x < 0

    x(x^3 - 1) < 0

    x(x-1)(x^2 + x + 1) < 0

    note that the factor (x^2 + x + 1) > 0 for all x (how can you check that the factor is always positive?)

    for the other two factors that can equal zero ... critical values are x = 0 and x = 1

    these two critical values divide the x-value number line into three regions ...

    x < 0 , 0 < x < 1 , and x > 0

    test a single x-value from each of the above intervals into the original inequality to see if this value makes the inequality true or false ...

    if true, then all values of x in that interval make the inequality true ... if false, then otherwise.
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  9. #9
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    Re: Inequality with higher degree

    x^4-x<0

    x^4-x=0

    This works as well just remember to put the strict inequity back in the answer.
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