1-solve-x-5-1-2-if-x-i-are-roots-of-this-equation-prove-that-i-x-i-0-3-prove-that-cos-2pi-5-cos-4pi-5-1-2-4-calculate-cos-4pi-5-interms-cos-2pi-5-then-find-its-values-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 31035 by abdo imad last updated on 02/Mar/18

1) solve x^5 =1 2) if x_i are roots of this equation prove that Σ_i x_i =0 3)prove that cos(((2π)/5)) +cos(((4π)/5)) =−(1/2) 4)calculate cos(((4π)/5)) interms cos(((2π)/5)) then find its values.

$$\left.\mathrm{1}\right)\:{solve}\:{x}^{\mathrm{5}} =\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{if}\:{x}_{{i}} \:{are}\:{roots}\:{of}\:{this}\:{equation}\:{prove}\:{that}\:\sum_{{i}} \:{x}_{{i}} =\mathrm{0} \\ $$$$\left.\mathrm{3}\right){prove}\:{that}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)\:+{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{4}\right){calculate}\:{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)\:{interms}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)\:{then}\:{find}\:{its} \\ $$$${values}. \\ $$

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1-solve-x-5-1-2-if-x-i-are-roots-of-this-equation-prove-that-i-x-i-0-3-prove-that-cos-2pi-5-cos-4pi-5-1-2-4-calculate-cos-4pi-5-interms-cos-2pi-5-then-find-its-values-

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