<s>[INST] Find the roots of the polynomial? (Cardano's Method) $y^3-\frac7{12}y-\frac7{216}$
This is part of Cardano's method, so I've gotten my first root to be:
$y_1=\sqrt[3]{\frac7{432}+i\sqrt{\frac{49}{6912}}}+\sqrt[3]{\frac7{432}-i\sqrt{\frac{49}{6912}}}$
I am at a loss on how to evaluate this. I know this is one of three real roots, but I don't know what to do now.
 [/INST] One can proceed as described above and find the three roots:
$\left\{\frac{1}{6} \left(\frac{7^{2/3}}{\sqrt[3]{\frac{1}{2} \left(1+3 i
   \sqrt{3}\right)}}+\sqrt[3]{\frac{7}{2} \left(1+3 i
   \sqrt{3}\right)}\right),-\frac{7^{2/3} \left(1+i \sqrt{3}\right)}{6\ 2^{2/3}
   \sqrt[3]{1+3 i \sqrt{3}}}-\frac{1}{12} \left(1-i \sqrt{3}\right) \sqrt[3]{\frac{7}{2}
   \left(1+3 i \sqrt{3}\right)},-\frac{7^{2/3} \left(1-i \sqrt{3}\right)}{6\ 2^{2/3}
   \sqrt[3]{1+3 i \sqrt{3}}}-\frac{1}{12} \left(1+i \sqrt{3}\right) \sqrt[3]{\frac{7}{2}
   \left(1+3 i \sqrt{3}\right)}\right\}$
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