Question Number 90750 by abdomathmax last updated on 25/Apr/20
$${let}\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0}\:\:{calculate} \\ $$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(\alpha^{{k}} \:+\beta^{{k}} \right) \\ $$$${B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(\alpha^{{k}} −\beta^{{k}} \right) \\ $$