Question 1183076
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(2x)\ +\ \cos(x)\ +\ 1\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2(x)\ -\ 1\ +\ \cos(x)\ +\ 1\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2(x)\ +\ \cos(x)\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\(2\cos(x)\ +\ 1)\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ 0\ \Right\ x\ =\ \pi n_1\ +\ \frac{\pi}{2},\ n_1\ \in\ \mathbb{Z}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos(x)\ +\ 1\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(x)\ =\ -\frac{1}{2}\ \Right\ x\ =\ \pi n_2\ +\ \frac{2\pi}{3},\ n_2\ \in\ \mathbb{Z}] 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ... \Right\ x\ =\ \pi n_3\ +\ \frac{4\pi}{3},\ n_3\ \in\ \mathbb{Z}] 


																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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