Question Number 152396 by mathdanisur last updated on 28/Aug/21
$$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} -\mathrm{x}+\mathrm{3}=\mathrm{0}\:\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{a};\mathrm{b}\:\:\mathrm{and}\:\:\mathrm{c} \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{monic}\:\mathrm{polynomial}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\:\mathrm{a}^{\mathrm{5}} \:;\:\mathrm{b}^{\mathrm{5}} \:\:\mathrm{and}\:\:\mathrm{c}^{\mathrm{5}} \:. \\ $$
Answered by mindispower last updated on 28/Aug/21
$${nwetoon}\:{identities}\:{to}\:{find}\:{a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{c}^{\mathrm{5}} ;\Sigma{a}^{\mathrm{5}} {b}^{\mathrm{5}} \\ $$$${anda}^{\mathrm{5}} {b}^{\mathrm{5}} {c}^{\mathrm{5}} \\ $$