Solve 2 cubic equations

**james_bond** · February 3rd 2010, 12:20 AM

$x^3-3x-1=0$
$x^3+x^2-2x-1=0$

**mr fantastic** · February 3rd 2010, 01:24 AM

Originally Posted by james_bond

$x^3-3x-1=0$
$x^3+x^2-2x-1=0$

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.)?

**james_bond** · February 3rd 2010, 11:30 PM

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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