<s>[INST] If α and β are the roots of the equation $3x^2+5x+4=0$, find the value of $α^3+β^3$ If α and β are the roots of the equation $3x^2+5x+4=0$, find the value of $α^3+β^3$
How can I factorize the expression to use the rule of sum and product of roots?
The answer is $\frac{55}{27}$
 [/INST] expanding $$\frac{1}{216} \left(-5-i
   \sqrt{23}\right)^3+\frac{1}{216} \left(-5+i
   \sqrt{23}\right)^3$$ we obtain $$\frac{55}{27}$$
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