Question Number 217857 by hardmath last updated on 22/Mar/25
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos20}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos80}°}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{cos160}°}\:=\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{3}\:\centerdot\:\sqrt[{\mathrm{3}}]{\mathrm{9}}\:−\:\mathrm{6}}{\mathrm{2}}} \\ $$
Answered by Frix last updated on 22/Mar/25
$$\mathrm{Staying}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{20}°}=−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{160}°}\:\Rightarrow \\ $$$$\mathrm{cos}\:\mathrm{80}°\:=\frac{\mathrm{3}}{\mathrm{2}}\sqrt[{\mathrm{3}}]{\mathrm{9}}−\mathrm{3}\approx.\mathrm{12} \\ $$$$\mathrm{But}\:\mathrm{cos}\:\mathrm{80}°\:\approx.\mathrm{17} \\ $$$$\Rightarrow\:\mathrm{false}\:\mathrm{claim} \\ $$
Answered by MathematicalUser2357 last updated on 29/Mar/25
$$× \\ $$