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Math Help - Solve 2 cubic equations

  1. #1
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    Solve 2 cubic equations

    • x^3-3x-1=0
    • x^3+x^2-2x-1=0
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  2. #2
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    Quote Originally Posted by james_bond View Post
    • x^3-3x-1=0
    • x^3+x^2-2x-1=0
    There are no simple solutions for the first and I haven't checked the second. How are you expected to solve them (eg. Cardano's cubic formula, use technology to get approximate solutions etc.)?
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  3. #3
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    I have to give the explicit answer not just numerical approximation. I can use whatever I know/find not just Cardano's method. Using Mathematica I've found 2 solutions to the first equation: 2\cos\left[\frac {\pi}9\right] and -\cos\left[\frac {\pi}9\right]+\sqrt 3\sin\left[\frac {\pi}9\right]. Waiting for ideas...
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