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Math Help - Inequalities. (1)

  1. #1
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    Inequalities. (1)

    Let x&y be real numbers such that : -2 \leq x \leq 1 and 1 \leq 3x-x^2+2y^2 \leq 22

    Show that : -4 \leq y \leq 4
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  2. #2
    A Plied Mathematician
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    I would start by letting f(x)=3x-x^{2}, and finding its extremes on the interval [-2,1]. What do you get?
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  3. #3
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    Finding extremes is a method in calculus.
    This is pre-calculus subforum.
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    -2<x<1

    -6<3x<3

    0<x^2<1

    -6<3x-x^2<2
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  5. #5
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    Quote Originally Posted by TWiX View Post
    Finding extremes is a method in calculus.
    You have a parabola, so you can do it with basic algebra.
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  6. #6
    A Plied Mathematician
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    Quote Originally Posted by Also sprach Zarathustra View Post
    -2<x<1

    -6<3x<3

    0<x^2<1

    -6<3x-x^2<2
    I think there is an error here. The correct inequality is

    -10\le 3x-x^{2}\le 2.

    Do you see how to get this?
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