Question Number 145162 by Skabetix last updated on 02/Jul/21
$${we}\:{have}\:{z}\:=\:{e}^{\frac{\mathrm{2}{pi}}{\mathrm{7}}{i}} \: \\ $$$${a}\:=\:{z}+\:{z}^{\mathrm{2}} \:+\:{z}^{\mathrm{4}} \:\:{and}\:{b}\:=\:{z}^{\mathrm{3}} \:+\:{z}^{\mathrm{5}} \:+{z}^{\mathrm{6}} \\ $$$${we}\:{know}\:\:{a}\:+\:{b}\:=\:−\mathrm{1}\:{and}\:\mathrm{1}−{b}={a} \\ $$$${find}\:{S}\:=\:{cos}\left(\frac{\mathrm{2}{pi}}{\mathrm{7}}\right)+\:{cos}\left(\frac{\mathrm{4}{pi}}{\mathrm{7}}\right)\:+\:{cos}\left(\frac{\mathrm{8}{pi}}{\mathrm{7}}\right) \\ $$$${thanks}\:{for}\:{help} \\ $$
Commented by gsk2684 last updated on 03/Jul/21
$$\mathrm{statements}\:\mathrm{in}\:\mathrm{hypothesis}\:\mathrm{are}\: \\ $$$$\mathrm{cotradicts}. \\ $$