# Thread: Solve 2 cubic equations

1. ## Solve 2 cubic equations

• $x^3-3x-1=0$
• $x^3+x^2-2x-1=0$

2. 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.)?

3. 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...