<s>[INST] Using Vieta's formula to find the sum of the roots for a given cubic equation. Vieta's formula states that, if a cubic equation has three different roots, the following is true:
$$\begin{eqnarray*}
x_1 + x_2 + x_3 &=& -b/a\\
x_1x_2 + x_1x_3 + x_2x_3 &=& c/a \\
x_1x_2x_3 &=& -d/a 
\end{eqnarray*}$$
Then, how is the following calculated?
$x_1^3$ + $x_3^3$ + $x_2^3$
 [/INST] Use that $$(a+b+c)^3=a^3+b^3+c^3+3ab(a+b)+3ac(a+c)+3bc(b+c)+6abc$$
$$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$$
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