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Thread: Absolute Value Equation

  1. #1
    Super Member harpazo's Avatar
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    Absolute Value Equation

    How many real numbers satisfy x^6 + |x| = 7?

    Set Up:

    x^6 + |x| - 7 = 0

    x^6 + x - 7 = 0

    Correct so far?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Absolute Value Equation

    Quote Originally Posted by harpazo View Post
    How many real numbers satisfy x^6 + |x| = 7?

    Set Up:

    x^6 + |x| - 7 = 0

    x^6 + x - 7 = 0

    Correct so far?
    You will actually end up with two equations. |x| is not always equal to x. For negative x we have |x| = -x.

    Anyway:
    For x < 0 we have $\displaystyle x^6 - x = 7$ and
    For 0 < x we have $\displaystyle x^6 + x = 7$

    -Dan
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  3. #3
    Super Member harpazo's Avatar
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    Re: Absolute Value Equation

    Quote Originally Posted by topsquark View Post
    You will actually end up with two equations. |x| is not always equal to x. For negative x we have |x| = -x.

    Anyway:
    For x < 0 we have $\displaystyle x^6 - x = 7$ and
    For 0 < x we have $\displaystyle x^6 + x = 7$

    -Dan
    I gotta solve both equations for x. Right?
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Absolute Value Equation

    Quote Originally Posted by harpazo View Post
    I gotta solve both equations for x. Right?
    Solving a 6th order equation is going to be problematic, to put it mildly. My suggestion would be to graph it and note how many real zeros you get. (There should be 0, 2, 4, or 6 of them.)

    I realize that means the comment about the absolute value was meaningless (you can plug the absolute value into the graphing calculator) but it needed to be corrected. Graph it and see what happens.

    -Dan
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  5. #5
    Super Member harpazo's Avatar
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    Re: Absolute Value Equation

    Thanks.
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