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Math Help - Cardano's Method

  1. #1
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    Cardano's Method

    Solve the qubic x^3 - 7x + 6 using Cardano's Method. Express all your
    answers as possible irrational numbers (i.e. no decimals!) and show your steps.

    Please help---this problem is driving me nuts!
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  2. #2
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    Re: Cardano's Method

    I haven't done this in a while but this may help

    Cardano's Method

    I'll see if I can work out a step or two to get you started.

    It looks like your teacher or textbook already did the first step for you, eliminating the square term by the substitution

    y = x + (b/3)a
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  3. #3
    Forum Admin topsquark's Avatar
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    Re: Cardano's Method

    I'll add to the number of ways to solve this. See this page. I usually use what's called "Vieta's Substitution." (A bit down the page.) And the trigonometric method (further down the page) has its points as well, though it's a bit more complicated. This is really nice if you need to show how many real roots the cubic has.

    -Dan
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