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Math Help - Silvanus P. Thompson Text problem

  1. #1
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    Question Silvanus P. Thompson Text problem

    Hi there,

    I am a Physics teacher and for a bit of fun I am working through Calculus made easy by Thompson. I have got stuck on some algebra on q.7 exercise X. The question asks " Find the maxima and minima of y = 3x /(x^2 - 3) + 0.5x + 5.
    So I have differentiated this and got (-3x^2 - 9)/(x^2-3)^2 + 5

    I then equated the differential to zero and tried to solve for x. I got the equation down to 12x^2 + 9 = x^4 but now I am stuck.. How do I simplify this to get x?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Haakon View Post
    Hi there,

    I am a Physics teacher and for a bit of fun I am working through Calculus made easy by Thompson. I have got stuck on some algebra on q.7 exercise X. The question asks " Find the maxima and minima of y = 3x /(x^2 - 3) + 0.5x + 5.
    So I have differentiated this and got (-3x^2 - 9)/(x^2-3)^2 + 5

    I then equated the differential to zero and tried to solve for x. I got the equation down to 12x^2 + 9 = x^4 but now I am stuck.. How do I simplify this to get x?
    Hello Haakon!

    I would recommend writing it as a quartic equation: x^4-12x^2-9=0. Now make the substitution z=x^2. This substitution lets us solve the quadratic equation z^2-12z-9=0. Solving for z, we get:

    z=\frac{12\pm\sqrt{144+36}}{2}\implies z=6\pm 3\sqrt{5}.

    But z=x^2, thus x^2=6\pm 3\sqrt{5}\implies x=\pm\sqrt{6\pm 3\sqrt{5}}.

    Hope this made sense!
    Last edited by Chris L T521; May 31st 2008 at 10:53 PM. Reason: typo... :(
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